[size=150]Select all the expressions that are equal to [math]\left(1.21\right)^{100}[/math]:[/size]

[size=150]From 1790 to 1860, the United States population, in thousands, is modeled by the equation [math]P=4,000\cdot\left(1.031\right)^t[/math] where [math]t[/math] is the number of years since 1790.[/size][br][br][size=100]About how many people were living in the U.S. in 1790? Show your reasoning.[/size]

What about in 1860? Show your reasoning.

What is the approximate annual percent increase predicted by the model?[br]

What does the model predict for the population in 2017? Is it accurate? Explain.[br]

What percent increase does the model predict each decade? Explain.[br]

Suppose [math]d[/math] represents the number of [i]decades[/i] since 1790. Write an equation for [math]P[/math] in terms of [math]d[/math] modeling the population in the US (in thousands).

What percent increase does the model predict each century? Explain.[br]

Suppose [math]c[/math] represents the number of centuries since 1790. Write an equation for [math]P[/math] in terms of [math]c[/math] modeling the population in the United States (in thousands).[br]

[size=150]In each case, $1,000 has been put in an interest-bearing bank account. No withdrawals or other deposits (aside from the earned interest) are made for 6 years.[/size][br][br]Sort the expressions that represent the same amounts of interest into groups. One group contains more than two expressions. One of the descriptions does not have a match. Write an expression that matches it. 

Without doing any calculations, rank these four possible changes in order of the increase in the interest they would yield from the greatest increase to the least increase:[br][br][list][*]Increase the starting amount by $100.[/*][*]Increase the interest rate by 1%.[/*][*]Let the account increase for one more year.[/*][*]Compound the interest every month instead of every two months.[/*][/list][br]Once you have made your predictions, calculate the value of each option to see if your ranking was correct.

30% increase

30% decrease

2% increase

2% decrease

0.04% increase

0.04% decrease

100% increase

[size=150]In 1990, the population p of India was about 870.5 million people. By 1995, there were about 960.9 million people. The equation [math]p=870.5\cdot\left(1.021\right)^t[/math] approximates the number of people, in millions, in terms of the number of years [math]t[/math] since 1990.[/size][br][br][size=100]By what factor does the number of people grow in one year?[/size]

If [math]d[/math] is time in decades, write an equation expressing the number of people, [math]p[/math], in terms of decades, [math]d[/math], since 1990.

Use the model [math]p=870.5\cdot\left(1.021\right)^t[/math] to predict the number of people in India in 2015.

The 2015, the population of India was 1,311 million. How does this compare with the predicted number?

[size=150]An investor paid $156,000 for a condominium in Texas in 2008. The value of the homes in the neighborhood have been appreciating by about 12% annually.[/size][br][br]Select [b]all [/b]the expressions that could be used to calculate the value of the house, in dollars, after [math]t[/math] years.

[size=150]A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a $30 purchase.[br][/size][br]Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?

[size=150]The expression [math]1,500\cdot\left(1.085\right)^3[/math] represents an account balance in dollars after three years with an initial deposit of $1,500. The account pays 8.5% interest, compounded annually for three years.[/size][br][br][size=100]Explain how the expression would change if the bank had compounded the interest quarterly for the three years.[/size]

Write a new expression to represent the account balance, in dollars, if interest is compounded quarterly.

[size=150]The function, [math]f[/math], defined by [math]f\left(t\right)=1,000\cdot\left(1.07\right)^t[/math], represents the amount of money in a bank account [math]t[/math] years after it was opened.[br][/size][br][size=100]How much money was in the account when it was opened?[/size]

When does the account value reach $2,000? 

Give an example of a domain for which the average rate of change is a good measure of how the function changes.

Give an example of a domain for which the average rate of change is not a good measure of how the function changes.

[size=150]The number of people, [math]P[/math], who can sit at the tables is a function of the number of tables, [math]n[/math].[/size][br][img]data:image/png;base64,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[/img][br]Explain why the equation [math]P=3n+2[/math] defines this function.

How many tables are needed if 47 people come to the party?

How many tables are needed if 99 people come to the party?

Write the inverse of this function and explain what the inverse function tells us.