Question

The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7

Answer 1

Answer:

Option 4 - 7%

Step-by-step explanation:

Given : The function $P(t) = 5000 (0.93)^t$ is the value of a motor scooter t years after it is purchased.

To find : Which of the following values show the annual depreciation of the value of the motor scooter?

Solution :

We are given a function p(t) which is represented as:

$P(t) = 5000 (0.93)^t$

Where, p(t) is the value of a motor scooter t years after it is purchased.

Depreciation is the amount that has been deducted from the cost of an item.

The rate of change is 1-0.93=0.07 i.e. 7%.

So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.

Therefore, The annual rate of depreciation is 7%.

So, option 4 is correct.

Answer 2

P(t) = 5,000 (1-r)t
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t

The annual depreciation rate is 7%