Question

Can any one help? Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes​ f(x) =​ g(x). ​f: initial value of 800 decreasing at a rate of 12​% ​g: initial value of 20 increasing at a rate of 12​%

Answer 1

The given exponential functions f(x) and g(x) will be equal for the value of x as 4.1466.

Explanation:

We need to give exponential function to the given constraints.

since f(x) is a decreasing function so

f(x) =
`a(1-r)^x`

where

a = Initial value

r = rate at which function is decreasing

as we are given the values of a and r such as a = 800 and r = 12%

upon substituting these values in the equation we get

f(x) =
`800(1-0.12)^x`

=
`800(0.88)^x`

similarly we will do for g(x) but the only difference in f(x) and g(x) will be that f(x) in a decreasing exponential function whereas g(x) is an increasing function.

g(x) =
`a(1-r)^x`

where a is initial value and r is the rate at which the function is increasing so upon substituting these values we get.

g(x) =
`20(1+0.12)^x` =
`20(1.12)^x`

Now,

we need to find the value of x for which f(x) and g(x) will be equal.

so

`800 (0.88)^x = 20(1.12)^x`

`40(0.88)^x = (1.12)^x`

x will be approximately 4.1466

Therefore the given exponential functions f(x) and g(x) will be equal for the value of x as 4.1466.