Modeling with Exponential Functions

The current population of Morristown is  $19,000$ and is growing at 1.75% annually. Which function models this?

•  $19,000\left(1.75\right)^t$  

•  $19,000\left(1+1.75\right)^t$  

•  $19,000\left(1+0.0175\right)^t$  

•  $19,000\left(1+0.000175\right)^t$  

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

In 1349, the Black Plague was contracted by one hundred million people. Every year after that, the number of cases due to the Black Plague decreased by  $27\%$ . Which function models this? 

•  $100,000,000\left(28\right)^t$  

•  $100,000,000\left(1.27\right)^t$  

•  $100,000,000\left(0.73\right)^t$  

•  $100,000,000\left(0.66\right)^t$  

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

The temperature in a freezing car begins at 10° F. Every 10 minutes, the temperature increases by 40%. What's the temperature (in Fahrenheit)  of the car 30 minutes after it has been started?

•  $10\left(1.4\right)^3$  

•  $10\left(1.4\right)^{30}$  

•  $10\left(0.6\right)^3$  

•  $10\left(41\right)^{30}$  

Tags

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

Mr. Savage has $8,000,000 in his bank account, which accrues 1.932% interest every 3 months. How much money will be in his bank account after 9 years?

•  $8,000,000\left(2.932\right)^{36}$  

•  $8,000,000\left(1.932\right)^9$  

•  $8,000,000\left(1.01932\right)^9$  

•  $8,000,000\left(1.01932\right)^{36}$  

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

You open a bank account with $1. The bank gives you four plans to choose from. Which plan will earn you the most money by the end of the year?

• Earn 100% interest 1 time per year

• Earn 50% interest 2 times per year

• Earn 25% interest 4 times per year

• Earn 5% interest 20 times per year

• All plans have the same effect

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.4

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

You take out a student loan for $80,000 with 2.75% annual interest to pay for your first year of college. This loan will cover all course fees and books. Which is the exponential growth equation to model this situation?

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

A rubber ball dropped on a small surface takes a sequence of bounces. Each bounce is half as high as the preceding one. If the ball is dropped from a height of 64 feet, determine the exponential decay equation to model the situation.

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

A rubber ball dropped on a small surface takes a sequence of bounces. Each bounce is half as high as the preceding one. If the ball is dropped from a height of 64 feet, determine the height of the ball after it hits the surface on the 5th bounce

• 486 feet

• 2 inches

• 2 feet

• 49.5 feet

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Your dad buys a rare quitar in 2015 for $10,000. Experts estimate that its value will increase 12% per year. Use the given graph to predict approximately how many years it will take for the initial value to double.

• 4 years

• 5 years

• 6 years

• 7 years

A new car depreciates about 15% each year. You purchase a new car for $35,000. Using the graph predict about how many years it will take for the value of the care to be $25,000.

• 7 years

• 5 years

• 2 years

• 1 year