Exponential Growth/Decay

vocab

100

Some types of functions ___________at a constant  percent rate. 

What is Increase/decrease?

200

A regularly seen example of exponential growth is _________ 

What is compound interest? 

This is when you split up an annual interest rate and

pay/earn interest multiple times per year.

300

pecial number e ≈ 2. 718282 called ___________

to represent _______.

What is Euler’s number and continuous growth?

400

What is the formula for Continuos Growth/Decay

What is f(x) = ae^rx?

growth

100

Does the function model exponential growth or decay?

h(t)=0.25 x 1.5^t

What Is Growth?

200

Miles' buys a new car for $16,200. The value of the car depreciates (decreases) at 14.25% per year. What will the value of the car be, to the nearest cent, in 6 years?

What is $6440.50?

300

What is the rate of change of f(x) = 6 (1.025)^x

What is .025=2.5%?

400

With the function f(x) = 8 (1.4)^x  evaluate the function if 5 years have passed? Round your answer to the nearest whole number

43

decay

100

Does the function model exponential growth or decay?

g(t)=1.7 x 0.8^t

What is Decay?

200

What is the rate of change of f(x) = 4(.85)^x

What is 1-.85= - .15 = 15%?

300

Please make a equation to represent this problem: If Kat buys a new phone that was $750 and it loses 5% of its value monthly how much will her phone be worth in 5 years?      

What is f(x) = 750 (1-.05)^{12 x 5}?  

400

Kat puts $10,000 into a high-yield savings account in 2026. The account has a yearly interest rate of 4.5%. How much money will be in the account in 2036?

What is $ 15,529.69?

Compound Interest/continuous growth and decay

100

What does n represent in the compound interest formula? 

What is n is the number of times compounded

200

What is the formula for compound interest

What is f(t)=a(1+r/n)^{n x t}?

300

Write make a equation to represent this problem. If Miles takes 3% of Kat’s sanity continuously how much sanity does Kat have left in 2 years assuming Kat starts with 100% sanity?    

1e^{-.03 x 2}  or  100e^{-3 x 2}

400

If Kat invests $200 into Miles’s Plumbing Company which returns 8% of her investment compounding quarterly, how much money will she have in 4 years?Round your answer to the second decimal point

What is f(x) = 200 (1+.084)⁴⁴ = $274.56?