calculus question

Question

Use the Fundamental Theorem of Calculus to find the average value of f(x)=e^0.4x between x=0 and x=2.

Answer: 1.531925

Find the average value on the graph. Finally give the exact x value for which f(x)=the average value f(x)=the average value.

Answer for the x value=

I am having trouble finding the x value. I got 40ln(20e^0.8-20) and it said it was wrong.

Answer 1

The problem is asking for the x value when f(x) = avg.

avg = 1.531925

e^0.4x = avg

0.4x = ln(avg)

x = 2.5ln(avg)

If you plotted the graph, you can see where f(x) = e^0.4x and y= avg intersect.