3. A car has a purchase price of $28,500. The value declines continuously at an

Question

3. A car has a purchase price of $28,500. The value declines continuously at an exponential rate of 22% annually a. What is an equation modeling the value of this car after t" years? a. b. What is its value after 7 years? (2) b c. How long will it take for its value to be $2500? 02) C. 4. A bacteria colony grows continuously at an exponential rate. There are initally 1.3 million present. After 5 days, there are 6.9 milion present. a. What is an equation modeling the number of bacteria present after "d" days? a. b. How many bacteria will be present after 9 days? C. How long will it take the number of bacteria to reach 95 million? C.

Explanation / Answer

3) the exponential function can be written as

a) y = 28500 ( 1-.22 )^t

y = 28500 (0.78)^t

b) value after 7 years

y = 28500 (0.78)^7

y = $ 5006.187

c) 2500 = 28500 (0.78)^t

2500/28500 = (0.78)^t

t = 9.8 years

it will take 9.8 years to reach $ 2500

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