Question

Is the value of makayla’s scooter growing or decaying A growingB decaying

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given exponential function

`f\mleft(x\mright)=13500\cdot0.89^x`

STEP 2: Explain the standard exponential function

Exponential function is given as

`y=a\cdot b^x`

where:

a is the initial or starting value of the function,

b is the growth factor or growth multiplier. b determines the rate at which the graph grows or decays.

STEP 3: Compare the given function with the standard exponential function

`\begin{gathered} \text{By comparison,} \\ a=13500 \\ b=0.89 \end{gathered}`

STEP 4: Mention the condition for determining a growth or decay in an exponential function.

If a is positive and b is greater than 1, then it is an exponential growth

If a is positive and b is less than 1 buth greater than 0, then it is an exponential decay.

STEP 5: Reach a conclusion

It can be seen from Step 3 that a is positive(13500) and b(0.89) is greater than zero but less than 1, therefore this implies according to the condition in step 4 that the value of the scooter is decaying.