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Andrew [12]
3 years ago
10

Suppose the function f has an initial value of 1,000 and a decay rate of 5%. Let the function g have an initial value of 400 and

increase at a growth rate of 17%. Estimate a value of x, to the nearest tenth, for which f(x) = g(x).

Mathematics
1 answer:
Montano1993 [528]3 years ago
6 0

Answer:

4.4 years

Step-by-step explanation:

we know that

The equation of a exponential decay function is given by

y=a(1-r)^x

where

a is the initial value

r is the rate of change

The equation of a exponential growth function is given by

y=a(1+r)^x

where

a is the initial value

r is the rate of change

step 1

Find f(x)

in this problem we have

f(x)=1,000(1-0.05)^x

f(x)=1,000(0.95)^x

step 2

Find g(x)

in this problem we have

g(x)=400(1+0.17)^x

g(x)=400(1.17)^x

step 3

we have

f(x)=1,000(0.95)^x

g(x)=400(1.17)^x

f(x)=g(x)

solve the system by graphing

The solution is the x-coordinate of intersection point

using a graphing tool

The solution is x=4.4 years

see the attached figure

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