Unit 4 Leap Review

If f(x)=2(3)ˣ+1, what is the value of f(2)?

19

Consider the following sequence and type the missing number. ​ 1, ,4,8,16.

2

The equation A=1300(1.02)⁷ is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation?

2% growth

Susan won $2,000 and invested it into an account with an annual interest rate of 3.2%. If her investment were compounded monthly, which expression best represents the value of her investment after t years?

2000(1.003)¹²ᵗ

Mike uses the explicit function shown to write a sequence of numbers. f(n)=(5)ⁿ⁺¹ ​ What are the first three numbers of Mike's sequence?

25, 125, 625

Camryn puts$400 into a savings account that earns 6% annually. The amount in her account can be modeled by C(t)=400(1.06)ᵗ where t is the time in years. Which expression best approximates the amount of money in her account using a weekly growth rate?

400(1.001121184)⁵²ᵗ

What is a common ratio of the geometric sequence whose first term is 5 and third term is 245?

7

In 1995, there were 80 birds in a park. The population increased by 5% each year. The number of birds in the park in 1997 was approximately what?

88

Biologists are studying a new bacterium. They create a culture with 100 of the bacteria and anticipate that the number of bacteria will double every 30 hours. Write an equation for the number of bacteria, B, in terms of the number of hours, t, since the experiment began.

B= 100(2)ᵗ𝄍³⁰

There are currently 50 vendors at the downtown farmers' market. The market is growing in popularity and the number of vendors is expected to increase by 12% each year relative to the previous year.​ Which statement correctly describes the equation that represents this situation?

It is y=50(1.12)ˣ because the base is 1.12 for a 12% increase.

A weight-loss reality show has 10 contestants. Each contestant can choose one of four program goals.​Which program has a constant rate per unit?

Lose 2% of the contestant's original weight each week.

A study of black bears in the Adirondacks reveals that their population can be represented by the function P(t)=3500(1.025)ᵗ, where t is the number of years since the study began. Which function is correctly rewritten to reveal the monthly growth rate of the black bear population?

P(t)=3500(1.00206)¹²ᵗ

A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by b(x)=850(1.025)ˣ.​​Which statement is the best interpretation of one of the values in this function?

The balance in the account increases at a rate of 2.5% each year.

Scientists are studying a bacteria sample. The function f(x)=245(1.12)ˣ gives the number of bacteria in the sample at the end of x days.​​Which statement is the best interpretation of one of the values in this function?

The number of bacteria increases at a rate of 12% each day.

A sequence is shown. 3, 6, 12, 24, 48, ... ​Which function, f(n), represents the nth term of the sequence, where f(1)=3?

f(n)=3⋅2ⁿ⁻¹

For which x-value does the value of f(x)=2ˣ-7 exceed the value of g(x)=3x²-7?

x=0