IM Alg1.5.15 Lesson: Functions Involving Percent Change
[size=150][size=100]All books at a bookstore are 25% off. Priya bought a book originally priced at $32. The cashier applied the storewide discount and then took another 25% off for a coupon that Priya brought. If there was no sales tax, how much did Priya pay for the book? Show your reasoning.[/size][/size]
To get a new computer, a recent college graduate obtains a loan of $450.She agrees to pay 18% annual interest, which will apply to any money she owes. She makes no payments during the first year.
How much will she owe at the end of one year? Show your reasoning.
Assuming she continues to make no payments to the lender, how much will she owe at the end of two years? [br]
Three years?
[size=150]To find the amount owed at the end of the third year, a student started by writing: [math]$\text{[Year 3 Amount]}=\text{[Year 2 Amount]}+\text{[Year 2 Amount]}\cdot (0.18)$[/math] and ended with [math]450\cdot\left(1.18\right)\cdot\left(1.18\right)\cdot\left(1.18\right)[/math]. [br][/size][br]Does her final expression correctly reflect the amount owed at the end of the third year? Explain or show your reasoning.[br]
Write an expression for the amount she owes at the end of [math]x[/math] years without payment.[br]
Start with a line segment of length 1 unit.
[size=150]Make a new shape by taking the middle third of the line segment and replacing it by two line segments of the same length to reconnect the two pieces. Repeat this process over and over, replacing the middle third of each of the remaining line segments with two segments each of the same length as the segment they replaced, as shown in the figure.[/size][br][img]data:image/png;base64,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[/img][br][br]What is the perimeter of the figure after one iteration of this process (the second shape in the diagram)?
After two iterations?
After [math]n[/math] iterations? Experiment with the value of your expression for large values of [math]n[/math].
Suppose three people each have taken loans of $1,000 but they each pay different annual interest rates. For each loan, write an expression, using only multiplication, for the amount owed at the end of each year if no payments are made.
Use graphing technology to plot the graphs of the account balances.
Based on your graph, about how many years would it take for the original unpaid balance of each loan to double?[br]
[size=150]The functions [math]a[/math], [math]b[/math], and [math]c[/math] represent the amount owed (in dollars) for Loans A, B, and C respectively: the input for the functions is [math]t[/math], the number of years without payments.[br][br]For each loan, find the average rate of change per year between:[/size][br][list][*]the start of the loan and the end of the second year[/*][/list]
[list][*]the end of the tenth year and the end of the twelfth year[br][/*][/list]
How do the average rates of change for the three loans compare in each of the two-year intervals?[br]
IM Alg1.5.15 Practice: Functions Involving Percent Change
In 2011, the population of deer in a forest was 650.
[size=150][size=100]In 2012, the population increases by 15%. [/size][/size]Write an expression, using only multiplication, that represents the deer population in 2012.
[size=150][size=100]In 2013, the population increases again by 15%. [/size][/size]Write an expression that represents the deer population in 2013.
If the deer population continues to increase by 15% each year, write an expression that represents the deer population [math]t[/math] years after 2011.
Mai and Elena are shopping for back-to-school clothes.
[size=150]They found a skirt that originally cost $30 on a 15% off sale rack. Today, the store is offering an additional 15% off. To find the new price of the skirt, in dollars, Mai says they need to calculate [math]30\cdot0.85\cdot0.85[/math]. Elena says they can just multiply [math]30\cdot0.70[/math].[/size][br][br]How much will the skirt cost using Mai’s method?
How much will the skirt cost using Elena’s method?
Explain why the expressions used by Mai and Elena give different prices for the skirt. Which method is correct?
One $1,000 loan charges 5% interest at the end of each year, while a second loan charges 8% interest at the end of each year.
Complete the table above with the balances for each loan. Assume that no payments are made and that the interest applies to the entire loan balance, including any previous interest charges. The scientific calculator below can be used for calculations.
Which loan balance grows more quickly?
How will this be visible in the graphs of the two loan balances [math]b[/math] and [math]c[/math] as functions of the number of years [math]t[/math]?
Use the applet below to create graphs representing [math]b[/math] and [math]c[/math] over time. The graph should show the starting balance of each loan as well as the amount of the loan after 15 years. Write down the graphing window needed to show these points.
[size=150]Lin opened a savings account that pays [math]5\frac{1}{4}\%[/math] interest annually and deposited $5,000.[/size][br][br]I[size=100]f she makes no deposits and no withdrawals for 3 years, how much money will be in her account?[/size]
A person loans his friend $500. They agree to an annual interest rate of 5%.
Write an expression for computing the amount owed on the loan, in dollars, after [math]t[/math] years if no payments are made.
[size=150]Select [b]all[/b] situations that are accurately described by the expression [math]15\cdot3^5[/math].[/size]
[size=150]Here are graphs of two exponential functions, [math]f[/math] an[/size]d [math]g[/math].[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKIAAACYCAYAAABnEzLQAAAN2ElEQVR4nO2dT2gbdxbHhxDKlmyRTnsdZwtLcQ8jutuE7G47atWedmupgQ2kDRmz0BSWgpwcTFLITg6L27As6kE+GXbsUGhSshmxJCbJOh2z9sGxG8tVcZQQx+PUalWskLHjmghj+O5BO2NJ1p+RPCP9JL0PzMGSPDOHD+/93u/3mzccHObZs2dOn5LoALhqPzAMA+Pj4zs+13Ud8Xi84LPV1VW8/fbbzt0d0TFUFREAOI7bIR3P85BlueCzs2fPguM4jI6OOnaDRGdgS0SPxwNN06y/FUUBz/MFv3n8+DH27dsHjuMgCIKT90h0ALZEFEWxIPrxPA9FUQp+09/fj+eeew4vv/wyOI5DLBZz8j6JNseWiJIkIRwOAwBkWd4R8dLpNARBwNDQEDiOw5dffolDhw45f7dE22JLRFmWIYoiDMOA1+stSNMA8PXXX+PZs2e4efMmOI7D6uoqUqkUdF134ZaJdsSWiJqmWelZFMWyv8sXkSBqwZaI8XgcoiiC5/kd0TAfEpGoF1siArkpHEmSKv6GRCTqxXZE5Diu6piPRCTqxfb0jVk1V4JEJOqlrIi6ruPcuXPw+/0QBAGGYVQ9GYlI1EtFEWVZRiQSsSUhQCIS9WO7WLEDiUjUC4lIMAGJSDABiUgwAYlIMAGJSDABiUgwAYlIMAGJSDABiUgwAYlIMAGJSDABiUgwAYlIMAGJSDABiUgwAYlIMAGJSDABiUgwAYlIMAGJSDABiUgwgeMi7nvlRSS+zzh5WqIDcFzEF8++gdcvX3TytEQH4LiI/LFfYv+F04jMpZ08NdHmOC7iL377AkJXj8A7NAP9adbJ0xNtjOMivvDizxCIdUO4mICozjt5eqKNcVzEvT/fg0CsG5cX/gtucIpSNGELV6Zv/vyfHkQTA5Cnl8ENTiGe2XDyMkQb4oqI/5iRcUI7DAAQ1Xn4LiVgZLecvBTRZrgi4s2FfyMQ68b65hr0p1l4hmYQnlhy8lJEm+GKiN8/XkYg1o3JH8YAAOriE3CDU1AXnzh5OaKNcG2J74Ov3sX5O2es76SxBZrSIcrimojDySjeu/mW9Z2R3YJwMQHfpYSTlyTaBNdEnMvcRiDWjfRGyvo+ntmg8SJREld33/RcPYDLCyMFv1GSKzReJHbgqohnpz7C2amPdvzOHC/S/CJh4qqI1x9dQSDWXfK35niR5hcJwGUR0xupgmmcfMz5xd5bD528BaJFcX2HdvE0Tj5aao3WowkADRCxeBqnmMhcmooXwn0RH6wmEYh148Fqsuz/UfFCNOThqaM3AjumcYqh4qWzaYiI5++csXbjlMPIboEfmaWVlw6lISJO/jC2Y5WlFObKC1XSnUfDnmsutcpSCrOSlqeXnbw1gnEaJqKd9GxiLgMqyRUnb49gmIaJaKbn9c01W+cKTyzRtE4H0dCWI3bTs0mjpnXi8ThCoRD8fj9kWXb1WkRpGipiLenZpBEyCoIASZKgaRp0XXftOkR5Giqi3eo5H3NDrVsyxuNxcBwHwzAcPzdhn4Z3A6s1PQOFu7udnPDWdR29vb3w+XwYHx+naNhEGi5iPekZcEdGWZbB8zxEUYQsy4jH446cl6idhotYT3o2MWUULjonI8/zUBTFkXMR9dOURp1HbwQwnIzWdQ0nI6NhGOA4jiIhAzRFxGhioOLWsGo4JaOmafB4PHX/P+EcTRHR3Lk9l7ld97X0p9ldyyjLMkRRrPseCOdoWg/tSju37bLbyGgWKUTzaZqI5oNVdpf8ypEvY63zjB6PB6qq7ur6hDM0TcT1zTX0XD2A64+u7Pq69Ux667pOE9kM0dTXW9Q7p1iKWmVUVRU8zztybWL3NFVE83mW3RQtxZhr09W2kEmSBEmSHLsusTua/sIfJ4qWYqSxhbL7GRVFgc/ng8fjoSU9hmi6iE4VLcWYj6n2FTV80nUdmqbR2JAxmi4ikNsIUe9KSyXMnd69tx7S04GMw4SI1R7C3w3mA1m+SwlqEsowTIhorrQ4MZVTCnMVhh7iZxcmRARyUzluRUUgN70THL1PD2UxCjMiOrH+bAfz3S/07DRbMCMiAJycOI5Tk5KTt1QSdfEJjRsZgykRzb7bbkdFoHDcSI+sNh+mRAQaFxWB3LjRnPwunm8kGgtzIjYyKpooyRUrVVNV3RyYExHIRcWTE8cduit75Kfqz76hDraNhkkRmxEVTcyq2q/epdWYBsKkiEAuKjq1RaxWtNQa+JFZKmQaCLMiur3aUg0ju2U1ggqN3qfo6DLMighsr7Y4vTOnFszo6KGxo6swLaL5OIEbO3NqIT86+tW7NAnuAkyLCACXF0bq7gzhNPHMBoSLCXCDUzg3naJ07SDMiwjkdnE3apLbDpG5NDxDM+i6EKdixiFaQkRzOqfUq9SaRf6qjKjOU7reJS0hIpBrU9Jz7WBTC5dSaKk1K133TSxRuq6TlhHRLFz+envna3dZwFwm9A7N0PixDlpGRGC7pR1LKTofI7sFeXoZnqEZ8COzGE5mmn1LLUNLiQiwm6LzyR8/dl2Ik5A2aDkR1zfXcPRGwJEqWtM0dHV1QRAEcBxnHU417tSfZklIm7SciMB2h4jdTHQbhgGv1wtN0wDkWpB4vV6H7rAQErI6LSkisD3RXe8OHUVRIAiC9bf5dgE3KSUkFTU5WlZEILcW3XPtYF2rLpFIBD6fz/q7kU0784WkKjtHS4u4vrmGD756Fye0wzUXL4ZhQBAE+Hw++P1+8Dzf8F7a+VW2+WRhp06Mt7SIQG67WM/VAzUXL4qiIBgMQtO0pjdzN7JbUJIr4EdmrY0VnfbsdcuLCOSKl56rB3B+9mPb/yOKIvr6+ph70Y+WWrMaAXRdiOPcdKojomRbiAhsT3bbkVHXdYRCIQiCAJ7nwXEcfD4fU0LqT7MFaTs0eh+xNt5g0TYiAtst7ipN6+i6vmM8aBgGRFFEOBxuxG3WjLr4xIqS3qEZ9E0std3Thm0lIrAt48i9wZLfl6uOW+ENA2aUNMeSvksJfPZNui1Sd9uJCGzLWCpNmy/5GR4exvj4OGKxGEKhEDweT0s174xnNiCNLVip23cp0dLzkm0pIlBdRkmSIIoiJElCJBJpKQmLURefFEjpV++2XKRsWxGBXAFjTu2wvEnCSYqlbJX03dYiAttTOye0w3iwmmz27TSUYim7LsTRN7HEZPXd9iIC2yswPdcONu056WYTz2wgPLFk7Sb3Ds0gOHqfmWjZESKaRBMDCMS6MfjtJx2TqkuhP81CSa4gOHq/IFr23nrYtIKno0QEtseN7918qym9dVhES61Bnl6GqM6DG5yyxpZmGm9ExOw4EYFcqj45cRyBWDeiiYGOjo7FGNktqItPCtI4NzgFfmQW0tgChpMZVybTO1JEk+uPrljR8cZ39JbSUhjZrZIR0zs0A796F+emUxj//umu03lHiwjkouP5O2cQiHXj1KRE6doG8cwGInNpSGML1iqPOc4Mjt6vS86OF9HkwWrSStckZG3kR838AsiUM/R/OSuNN0nEIuYyt0lIByiWM3+8aa7+9N56aEVPErEM+UKaY0gqanaPllqDklxBeGIJojq/HT2dvEg7iWjyYDVpjSF7rh3E+dmPKUo6jJHdIhHtsr65huuPruCDr961ouTgt5903LKhW5CIdZDeSCGaGMDRG4GCSDmZvkXpu05IxF2S3kjh8sKINZ4MxLpxQjuMwW8/ITFrgER0kPXNNUz+MIZoYsBK4WYaPz/7Mf718ALmHk+TnCUgEV1kfXMNc5nbGE5GcXLiOHquHiiQ89SkhJF7g7jxndrxgpKIDSa9kbLkPH/nTEFKz0/tJyeOY+TeIIaTUUymb2Hu8XRbFEYbG6XXqUlERjCj5/VHVzCcjOLs1Ec4OXHcKohKyXpqUsKpSQnRxIAl7b8eXsBc5nbuYFDeL774Av39/VhZKWwgQCK2CKaoc5nbuLwwguFktEDYStIWHz3XDuLUpGS9CTb/GLk3aB3DyWjB3yP3Bq3oXMtR3Jvo2LFjeP7559HX14cff/wRQA0izs/P49VXX614vPTSS9i3bx9ee+01+P1+Opp9/OF1+P/0++3jvd/hjb8c3HmED+AN+ddljzcjPrwZFRw9Dv39V3jlbzx+M7Aff/znIfsiLi8vo7+/v+Jx5MgRcByH06dPQ5ZlOugoeXz44YfYu3cv9uzZg/fffx+Li4uUmonG8tNPP2H//v145513MD8/b31uW0TDMKzeMIZhlGxeRCIS1fj8888xNTW143NbIqqqCkmSoOs6ZFmGJElW3+ne3l7rdyQiUS9VRVQUxWpOJIpiQfOicDgMjuOsPtQkIlEvFUVUVRXBYBAArIFmPoZhgOM463MSkaiEYRjweDxW4AKAYDCIYDBYXkSz676u69B1HaIoluwPIwgCiUjYRpIkSJIEIBfcBEHIBbRy/2C29q2GIAiIRCIASESiOrquW++y8Xg8VsFbVkS7/QI5jrNORiISdpAkCRzHFdQbZUXkeb6qiKqqFjS91HUdn3766a5vlGhfDMNAV1cXvF5vwVCvrIiCIFRt5SuKYsHAkyAqYRgGfD4fZFnekXHLihgMBndYm08kEnHsnXVEZyBJklV3mJ17TcqKqGmaNWFdLKMsyyQhURP5FbIJz/OWRxXnERVFAcdx6OrqQigUQigUQjgcZuo1EER7YGuJLx6PQ9O0lu4zTbCNu6/jJAibkIgEE5CIBBOQiAQT/A9eZC7FIjL9IQAAAABJRU5ErkJggg==[/img][br][br]If [math]f\left(x\right)=100\cdot\left(\frac{2}{3}\right)^x[/math] and [math]g\left(x\right)=100\cdot b^x[/math], what could be the value of [math]b[/math]?
[size=150]The real estate tax rate in 2018 in a small rural county is increasing by [math]\frac{1}{4}\%[/math]. Last year, a family paid $1,200.[br][/size][br]Which expression represents the real estate tax, in dollars, that the family will pay this year?
Two inequalities are graphed on the same coordinate plane.
[img]data:image/png;base64,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[/img][br]Select [b]all[/b] of the points that are solutions to the system of the two inequalities.