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

Answer:

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

Step-by-step 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.