Exponential Growth and Decay

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population.

Which function can be used to determine the number of deer, y, in this population at the end of t years?

• $y=1500(1-0.015)^t$

• $y=1500(0.015)^t$

• $y=1500(1+0.015)^t$

• $y=1500(1.5)^t$

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CCSS.HSF.LE.A.2

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month.

At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

• $f(x)=417(1-0.0375)^x$

• $f(x)=417(1-3.75)^x$

• $f(x)=417(1+0.0375)^x$

• $f(x)=417(1+3.75)^x$

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CCSS.HSF.LE.A.2

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased by 5% per year. How much is the home worth today?

• $176,783.29

• $424,527.63

• $57,357.75

• $532,041,076.80

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CCSS.HSF.BF.A.2

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute.

Which function can be used to model the number of bacteria in the colony after x minutes?

• $f(x)=12000(1+14.9)^x$

• $f(x)=12000(1-14.9)^x$

• $f(x)=12000(1+0.149)^x$

• $f(x)=12000(1-0.149)^x$

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CCSS.HSF.LE.A.2

A population of fish starts at 8,000 and decreases by 6% per year.

What is the fish population in 10 years?

• $14,327$

• $4,309$

• $839$

• $7,680$

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

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CCSS.HSF.BF.A.2

Your credit card balance is $1,253. The credit card company charges 3% interest compounding annually. Assuming you make no payments, how much would you owe after 10 years?

• y = 1253(1.03)¹⁰

• 1253 = P(1.03)¹⁰

• I = 1253(0.03)10

• y = 1253(1.3)¹⁰

Cassandra bought an antique dresser for $500. If the value of her dresser increases 6% annually, what will be the value of Cassandra's dresser at the end of 3 years to the nearest dollar?

• $415

• $590

• $596

• $770

The current student population of the Brentwood Student Center is 2,000. The enrollment at the center decreases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years'?

• 432

• 1769

• 2250

• 5488

Dylan invested $600 in a savings account at a 1.6% annual

interest rate. He made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years.

• $580.95

• $423.36

• $807.36

• $619.35