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?

• $y=1500(1-0.015)^t$

• $y=1500(0.015)^t$

• $y=1500(1+0.015)^t$

• $y=1500(1.5)^t$

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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?

• $f(x)=417(1-0.0375)^x$

• $f(x)=417(1-3.75)^x$

• $f(x)=417(1+0.0375)^x$

• $f(x)=417(1+3.75)^x$

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

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?

• $f(x)=12000(1+14.9)^x$

• $f(x)=12000(1-14.9)^x$

• $f(x)=12000(1+0.149)^x$

• $f(x)=12000(1-0.149)^x$

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Some banks charge a fee for a savings account that is left inactive for an extended period of time. 

The equation  $y=5000(0.98)^x$   represents the amount remaining, y, of one account that was left inactive for a period of x years. 

What does the number 5000 represent in this situation?

• A fee charged for an inactive account

• The percent of money in the account after x years

• The amount of money in the account initially

• The amount of money in the account after x years

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.B.5

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

What is the fish population in 10 years?

• $14,327$

• $4,309$

• $839$

• $7,680$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Classify the model as Exponential GROWTH or DECAY.

 $A=1200(.85)^6$  

• Growth  $y=a\left(1+r\right)^t$  

• Decay  $y=a\left(1-r\right)^t$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

Classify the model as Exponential GROWTH or DECAY.

 $A=10(1.01)^3$  

• Growth  $y=a\left(1+r\right)^t$  

• Decay  $y=a\left(1-r\right)^t$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

Classify the model of an Exponential GROWTH.

•  $y=a\left(1+r\right)^t$  

•  $y=a\left(1-r\right)^t$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Classify the model of an Exponential DECAY.

•  $y=a\left(1+r\right)^t$  

•  $y=a\left(1-r\right)^t$  

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5