Which equation do you think the graph represents? Use the graph to support your reasoning.[br][list][*][math]y=120+\left(3.7\right)\cdot x[/math][br][/*][/list][list][*][math]y=120\cdot\left(1.03\right)^x[/math][br][/*][/list]
What information might help you decide more easily whether the graph represents a linear or an exponential function?[br]
[size=150]investing in government bonds that offer 2% simple interest, or investing in a savings account at a bank, which charges a $20 fee to open an account and pays 2% compound interest. Both options pay interest annually.[/size][br][size=150][br]Here are two tables showing what they would earn in the first couple of years if they do not invest additional amounts or withdraw any money.[/size][br]
Bonds: How does the investment grow with simple interest?
Savings account: How are the amounts $999.60 and $1,019.59 calculated?[br]
For each option, write an equation to represent the relationship between the amount of money and the number of years of investment.[br]
Which investment option should the family choose? Use your equations or calculations to support your answer.
[size=150][math]f(x)=2x[/math] and [math]g(x)=(1.01)^x[/math][/size]
Based on the table of values, which function do you think grows faster? Explain your reasoning.[br]
Which function do you think will reach a value of 2,000 first? Show your reasoning. If you get stuck, consider increasing [math]x[/math] by 100 a few times and record the function values in the table.[br]
Consider the functions [math]g\left(x\right)=x^5[/math] and [math]f\left(x\right)=5^x[/math]. While it is true that [math]f\left(7\right)>g\left(7\right)[/math], for example, it is hard to check this using mental math. Find a value of [math]x[/math] for which properties of exponents allow you to conclude that [math]f\left(x\right)>g\left(x\right)[/math] without a calculator.