Exponential Growth & Decay WP

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

• $0.29
• $2,900,000,000
• $46,704.79
• $145,000

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

• Increasing
• Decreasing

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1+ 0.15)^x

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(1 - 0.30)^x

• y=30(5000)^x

• y=5000(1 + 0.30)^x

• y=5000x^x

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

• $23,219.72

• $136.72

• $51,710.94

• $16,710.94

Change 6.75% to a decimal.

• 67.5
• .675
• 675
• .0675

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x

Connor bought a brand new Ford F-150 for $45,000.  Unfortunately, the value of the truck depreciates at a rate of 1.3% per month.  Which equation shows the value of the truck?

• 45,000(1.3)^x
• 45,000(1.013)^x
• 45,000(.987)^x
• 45,000(.013)^x

Dominic invested $19,000 in an account paying an interest rate of 6.1% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 16 years?

• $50,000

• $60,000

• $70,000

• $80,000

Answer explanation

Using the formula for compound interest A = P(1 + r/n)^(nt), where P = 19000, r = 0.061, n = 12, and t = 16, we find A ≈ 70000. Thus, the amount in the account after 16 years is approximately $70,000.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 1 year? Round to the nearest whole number.

Mathematical Equivalence

ON