Modeling Exponential Growth and Decay wk 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?

• $f\left(x\right)=80000\left(12.75\right)^x$

• $f\left(x\right)=80000\left(1.275\right)^x$

• $f\left(x\right)=80000\left(1.0275\right)^x$

• $f\left(x\right)=80000\left(.9725\right)^x$

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. How much money will you have to pay back for this loan when you graduate in 4 years (rounded to the nearest dollar)?

• $2,114,125,313

• $211,413

• $89,170

• $71,556

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.

•  $f\left(x\right)=64\left(1.5\right)^x$ 

•  $f\left(x\right)=64\left(.05\right)^x$ 

•  $f\left(x\right)=64\left(.5\right)^x$ 

•  $f\left(x\right)=64\left(.95\right)^x$ 

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

Your first credit card charges you 16.99% annual interest compounded weekly. If it takes you 10 years to pay off a $149 TV that you paid for using your credit card. Determine the exponential growth equation to model the situation.

•  $f\left(x\right)=149\left(11.699\right)^{52x}$ 

•  $f\left(x\right)=149\left(1.1699\right)^x$ 

•  $f\left(x\right)=149\left(1+\frac{.1699}{52}\right)^{52x}$ 

•  $f\left(x\right)=149\left(1-\frac{.1699}{52}\right)^{52x}$ 

Your first credit card charges you 16.99% annual interest compounded weekly. If it takes you 10 years to pay off a $149 TV that you paid for using your credit card. Determine the amount of money your would have actually spent on the TV after the 10 years (rounded to the nearest dollar).

• $210

• $716

• $813

• $28

You buy your first house for $275,000. The interest rate compounded monthly is 3.5%. If you have a 15 year mortgage, determine the exponential growth equation to model the situation.

•  $f\left(x\right)=275000\left(4.5\right)^x$ 

•  $f\left(x\right)=275000\left(1.35\right)^x$ 

•  $f\left(x\right)=275000\left(1+\frac{.035}{12}\right)^{12x}$ 

•  $f\left(x\right)=275000\left(1-\frac{.035}{12}\right)^{12x}$ 

You buy your first house for $275,000. The interest rate compounded monthly is 3.5%. If you have a 15 year mortgage, determine the amount of money actually spent on your house over the 15 year period. 

• $1,727,907

• $5,529,302

• $390,044

• $193,690

A new car depreciates about 15% each year. You purchase a new car for $35,000. Which exponential decay equation models this situation?

•  $f\left(x\right)=35000\left(-15\right)^x$ 

•  $f\left(x\right)=35000\left(.985\right)^x$ 

•  $f\left(x\right)=35000\left(.85\right)^x$ 

•  $f\left(x\right)=35000\left(1.15\right)^x$ 

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