11.

Question

Function 1: f(x) = 32x + 5

Function 2:

Desmos Link

(1 point)
Function
1
has a greater rate of change.
Question 13
12.

Salim purchased a motorcycle and it depreciates each year. Its depreciation is represented by the function f(x) = 14000(1−0.09)x


When will the motorcycle be worth $7000?

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(1 point)
Responses

6.7 years
6.7 years

7 years
7 years

7.3 years
7.3 years

8 years

Answer 1

To determine when Salim's motorcycle will be worth $7000, we want to solve the following equation based on the depreciation function:

\[ f(x) = 14000(1 - 0.09)^x \]

Setting \( f(x) \) equal to $7000:

\[ 7000 = 14000(1 - 0.09)^x \]

First, simplify the equation:

\[ \frac{7000}{14000} = (1 - 0.09)^x \]

This simplifies to:

\[ 0.5 = (0.91)^x \]

Now, we will take the logarithm of both sides to solve for \( x \):

\[ \log(0.5) = x \cdot \log(0.91) \]

Now, we can isolate \( x \):

\[ x = \frac{\log(0.5)}{\log(0.91)} \]

Now, using a calculator:

\[ \log(0.5) \approx -0.3010 \] \[ \log(0.91) \approx -0.0434 \]

Now, calculate \( x \):

\[ x \approx \frac{-0.3010}{-0.0434} \approx 6.93 \]

Thus, the motorcycle will be worth $7000 in approximately 7 years.

So the correct response from the given options would be:

7 years.