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Question Determine if the car's value follows a linear or exponential function. Then find the slope or growth factor.
Malik bought a car for $15,000\$15,000. Its value drops by 15%15\% annually. The function is v(t)=$15,000⋅(0.85)tv(t) = \$15,000 \cdot (0.85)^t. The growth factor is 0.850.85.

Studdy Solution

STEP 1

Assumptions
1. The initial value of the car is $15,000.
2. The car's value decreases by 15% each year.
3. A linear function has a constant rate of change (slope).
4. An exponential function has a constant percentage rate of change (growth factor).

STEP 2

Identify the type of function based on the given information.
Since the car's value decreases by a constant percentage (15%) each year, the function representing the car's value over time is an exponential decay function, not a linear function.

STEP 3

Determine the growth factor for the exponential function.
The growth factor in an exponential decay function is given by 1−decay rate1 - \text{decay rate}.

STEP 4

Convert the percentage of the decay rate to a decimal.
15%=0.1515\% = 0.15

STEP 5

Calculate the growth factor using the decay rate.
Growth factor=1−Decay rateGrowth\, factor = 1 - Decay\, rate
Growth factor=1−0.15Growth\, factor = 1 - 0.15

STEP 6

Complete the calculation for the growth factor.
Growth factor=1−0.15=0.85Growth\, factor = 1 - 0.15 = 0.85
The function is exponential. The growth factor is 0.850.85.

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