7.1 - 7.2 Exponential Models

7.1 - 7.2 Exponential Models

Application Problems

Exponential Growth & Decay Models

When a real-life quantity increases or decreases by a fixed % each year.

r = % increase or decrease

a = initial amount

t = time

Multiple Choice

You buy a new car for $25,000. The value of the car decreases (depreciates) by 15% per year. What equation would model the car's value t years from now?

• $y=25,000\left(1.15\right)^t$

• $y=25,000\left(0.85\right)^t$

• $y=.15\left(25,000\right)^t$

• $y=.85\left(25,000\right)^t$

Multiple Choice

Shota invests $2000 in a certificate of deposit that earns 2% in interest each year.

Which equation models the total value V(t), in dollars, of the investment t years from now?

• $V\left(t\right)=2000\left(.98\right)^t$

• $V\left(t\right)=2000\left(1.2\right)^t$

• $V\left(t\right)=2000\left(1.02\right)^t$

• $V\left(t\right)=.02\left(2000\right)^t$

Multiple Select

Which function(s) shown represent exponential growth? 

 (Check all that apply)

•  $f\left(t\right)=20\left(0.7\right)^t$  

•  $g\left(t\right)=2000\left(1.20\right)^t$  

•  $h\left(x\right)=\frac{1}{2}\left(4\right)^x$  

•  $j\left(x\right)=50\left(\frac{1}{2}\right)^x$  

Multiple Choice

The spotted lantern fly population went up 500% from 2019 to 2020 in the Philadelphia area.

There were approximately 5,600 lantern flies in 2019. If the population continues to increase at the same rate, how many will be present in 2021?

• 201,600

• 28,000

• 56,000

• 16,800

Compound Interest Model

P = Principal (starting amount of money)

r = annual interest (% → decimal)

n = compounding number per year

t = time

Multiple Choice

You deposit $3,500 in an account that earns 2.5% annual interest. Which equation models the amount t years after you deposit the money, if the money is compound quarterly?

• $A=3500\left(1+\frac{2.5}{25}\right)^{25t}$

• $A=3500\left(1+\frac{0.25}{4}\right)^{4t}$

• $A=3500\left(1+\frac{2.5}{4}\right)^{4t}$

• $A=3500\left(1+\frac{0.025}{4}\right)^{4t}$

Multiple Choice

You decide to invest your birthday money that you've been saving, a whooping $5000, into a mutual fund that earns 2% annual interest, compounded monthly. Approximately how much money will you have in 5 years?

• $5,525.39

• $5,100.92

• $13,479.85

• $25,504.61