100 POINTS Exponential and Logarithmic Models
In this activity, you will formulate and graph exponential and logarithmic functions and describe the relationship between the two functions.

Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees in the forest that will be infected after t years.
f(t)=e^0.4t

Part A
Question
Graph the function f(t)=e^0.4t

Part B
Question
The scientists believe the forest will be seriously damaged when 21 or more of the forest’s 200 oak trees are infected by oat wilt. According to their model, how many years will it take for 21 of the trees to become infected?

Type the correct answer in the box. Use numerals instead of words. Round your answer to the nearest tenth.

It will take approximately -blank- years for 21 of the trees to become infected.

Part C
Question
Rewrite the exponential model as a logarithmic model that calculates the number of years, g(x) , for the number of infected trees to reach a value of x.

Enter the correct answer in the box.

Part D
Question
Graph the logarithmic function that models the number of years, g(x) , for the number of infected trees to reach a value of x.

Part E
Compare the features of the graphs of functions f and g. Then use your observations to describe the relationship between the domains and ranges of the two functions.