Question

What exponential functions represents a situation in which the initial value is 175 and the rate of decay is 20%

Answer 1

`y=175(0.8)^t`

Explanation:

Given : The initial value is 175 and the rate of decay is 20%

To find : Exponential functions represents a given situation.

Solution :

The general form of exponential function when decay is there

`y=a(1-r)^t`

Where,

y is the final amount

a is the initial value

r is the rate of decay

t is the time

(1-r) is the decay factor

According to given situation,

Initial value a=175

Decay rate is 20%

r=20%=0.2

Substitute the value,

`y=175(1-0.2)^t`

`y=175(0.8)^t`