Alg1.5 End-of-Unit Review

At the beginning of the year, a small town's library had 8,000 books. Throughout the year, the library's collection grew by 3% each month. Which expressions represent the number of books, in thousands, owned by the library 4 years later if it continues to grow at this rate? Select all the correct expressions.

• 8,000⋅((1+0.03)¹²)⁴

• 8,000⋅(1+0.03)⁽¹²⁾⁴⁸

• 8,000⋅(1.03)⁴

• 8,000⋅(1.03)⁴⁸

• 8,000⋅(0.03)⁴⁸

Answer explanation

The correct expressions are 8,000⋅((1+0.03)^12)^4 and 8,000⋅(1.03)^48, as they correctly calculate the number of books owned by the library 4 years later with a 3% monthly growth rate.

Tags

CCSS.HSF.BF.A.2

A small town's population was 5,000 at the start of the year. If the population increases by 2% every month, what expressions accurately represent the population, in thousands, 3 years later assuming the growth rate remains constant?

• 5,000⋅((1+0.02)³⁶

• 5,000⋅(1+0.02)(12)³⁶

• 5,000⋅(1.02)³

• 5,000⋅(1.02)³⁶

• 5,000⋅(0.02)³⁶

Answer explanation

Choose the expressions that accurately represent the population growth over 3 years. The correct choices are 5,000⋅((1+0.02)^36) and 5,000⋅(1.02)^36.

Tags

CCSS.HSF.BF.A.2

The function p(y)=150⋅(0.97)^y models the price in dollars, p, of a specific enzyme used in research. y represents the number of years since 2015. Does the price of the enzyme increase or decrease over time?

• The price increases.

• The price decreases.

Answer explanation

The price of the enzyme decreases over time as the exponential function decreases with increasing y, representing years since 2015.

Tags

CCSS.HSF-IF.C.8B

Upon the birth of her daughter, a mother wishes to start a savings account with an initial deposit of $200. She intends to let the amount grow until her daughter turns 21, without making any additional deposits or withdrawals. She is considering two savings options:

Option 1: A savings account where the balance increases by $25 each year.

Option 2: A savings account that earns an annual interest rate of 8%.

Which savings option will provide the larger amount by the time her daughter turns 21?

• Option 1

• Option 2

Tags

CCSS.HSF.BF.A.2

The population of a city increases by 5% every year. If its population today is 300,000, what expression will represent its population in 2 years?

• 300,000⋅(0.05)

• 300,000⋅(1.05)

• 300,000⋅(1.05)⋅(2)

• 300,000⋅(1.05 )²

Answer explanation

The correct expression to represent the city's population in 2 years is 300,000⋅(1.05 )^2, as the population increases by 5% each year for 2 years.

Tags

CCSS.HSF.BF.A.2

For which function does f decrease by 15% every time x increases by 1?

• f(x)=0.15^x

• f(x)=0.85^x

• f(x)=15^x

• f(x)=85^x

Answer explanation

The function that decreases by 15% every time x increases by 1 is f(x)=0.85^x, as 0.85 represents a decrease of 15% from 1.

Tags

CCSS.HSF.LE.A.2

A car's value decreases by 20% each year. If the current value of the car is $15,000, what will be its value after 3 years?

• $8,640

• $9,600

• $10,560

• $12,000

Answer explanation

To find the value after 3 years, we calculate 80% of the original value after each year. After 3 years, the value will be $8,640.

Tags

CCSS.HSF.BF.A.2

If a savings account offers an annual interest rate of 3%, and you deposit $5,000, how much money will be in the account after 1 year, assuming no withdrawals?

• $5,000

• $5,150

• $5,250

• $5,500

Answer explanation

After 1 year, the account will have $5,000 + ($5,000 * 3%) = $5,000 + $150 = $5,150. Therefore, the correct answer is $5,150.

Tags

CCSS.HSF.BF.A.2

The population of a certain species of fish in a lake increases at a rate of 10% per year. If the current population is 2,000 fish, what will be the population after 5 years?

• 3,000 fish

• 3,200 fish

• 3,221 fish

• 3,105 fish

Answer explanation

The population after 5 years can be calculated by multiplying the current population by 1.10^5, which equals 3,221 fish. Therefore, the correct answer is 3,221 fish.

Tags

CCSS.HSF.BF.A.2

A tree grows at a steady rate of 8% per year. If it is currently 10 feet tall, how tall will it be in 3 years?

• 12.6 feet

• 12.96 feet

• 13.5 feet

• 14.26 feet

Answer explanation

To calculate the height in 3 years, we use the formula: 10 * (1 + 0.08)^3 = 12.6 feet. Therefore, the tree will be 12.6 feet tall in 3 years.

Tags

CCSS.HSF.BF.A.2