Question

The function p(t) represents the value of a new car t years after it was manufactured.

p(t)=24,525(0.94)^t



What does the value 0.94 represent in this situation?

The value of the car increases by 94% each year.

The initial value of the car is 0.94.

The value of the car is 0.94 times the value of the car the previous year.

The value of the car decreases by 94% each year.


I think its D

Answer 1

The value of the car is 0.94 times the value of the car the previous year.

Answer 2

Option C is correct

The value of the car is 0.94 times the value of the car the previous year.

Explanation:

Given the function:

`p(t) = 24,525(0.94)^t`

where,

p(t) represents the value of a new car

t is the number of years.

We have to find the value 0.94 represent in this situation.

For t =0 years.

Initial value of car p(0) is 24,525

For t = 1 years

`p(1) =24,525 \cdot 0.94`

For t = 2 years

`p(2) =24,525 \cdot (0.94)^2` and so on...

Since;

`(p(2))/(p(1)) = 0.94`

⇒
`p(2) = 0.94 \cdot p(1)`

In general:

`p(t) = 0.94 \cdot p(t-1)` where, t is the number of years.

⇒the value of the car is 0.94 times the value of the car the previous year.