IM Alg1.5.18 Lesson: Expressed in Different Ways

Select all the expressions that are equal to :

From 1790 to 1860, the United States population, in thousands, is modeled by the equation where is the number of years since 1790. About how many people were living in the U.S. in 1790? Show your reasoning.

What about in 1860? Show your reasoning.

What is the approximate annual percent increase predicted by the model?

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

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

Suppose  represents the number of decades since 1790. Write an equation for in terms of modeling the population in the US (in thousands).

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

Suppose  represents the number of centuries since 1790. Write an equation for  in terms of  modeling the population in the United States (in thousands).

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. 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:

• 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.