Question

Pls help asap!

Determine the initial value and decay rate for the equation:
f(t) = 12.5 (0.625) ^t

Answer 1

The initial value is 12.5

Decay rate is 37.5 %

Solution:

Given that equation is:

`f(t) = 12.5(0.625)^t`

We have to find the initial value and decay rate

The equation for decay is given as:

`y = a(1-b)^x`

Where,

y is the final amount

a is the initial value

b is the rate of decay

x is the number of years

On comparing given equation and above general equation,

a = 12.5

Thus initial value is 12.5

Also,

`1-b = 0.625\\\\b = 1-0.625\\\\b = 0.375`

Thus decay rate = 0.375 x 100 = 37.5 %

Thus decay rate is 37.5 %