In this activity, you will use technology to develop an exponential model of a data set and then use the model to make predictions. Over a 10-year period, the scientists recorded the number of oak trees infected with oak wilt in the forest. Their data is in the table.

Years Number of Trees
0 1
2 1
4 3
6 9
8 17
10 31

Part A
Plot the data from the table on the graph, where x represents the number of years and y represents the number of trees infected by oak wilt. Then fit an exponential function to the data.

Part B
Using the Graphing tool, write the exponential function that best models the number of trees infected, f(x) in terms of years, x. Round values to the nearest hundredth.

Part C
Consider the exponential function modeling the data. According to the function, how many of the trees in the forest will have been infected by oak wilt by year 12?
Round your answer to the nearest whole number.

According to the function modeling this situation, all 200 trees will be infected by oak wilt approximately years after the first tree was infected.​
The function predicts that by year 12, around trees __ will have been infected by oak wilt.

Part D
The scientists want to predict how long it will take all 200 of the oak trees in the forest to become infected with oak wilt.

According to the function modeling this situation, all 200 trees will be infected by oak wilt approximately ___ years after the first tree was infected.​