Question

Model the pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x)=g(x).

Answer 1

At x= 20.10723974, both f(x)=g(x)

Explanation:

f(x) = 300(1-0.04)^x = 300(0.96)^x

g(x) = 60(1+0.04)^x = 60(1.04)^x

now equate both of them and calculate x

300(0.96)^x = 60(1.04)^x

5(0.96)^x = (1.04)^x

ln(5) + x ln(0.96) = x ln(1.04)

x={ln(5)}/{ln(1.04)-ln(0.96)}

x= 20.10723974