Oakville 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 affected after t years F(t)=e^0.4t
Part a
Graph the function F(t)=e^0.4t
Part b
The scientist believe the Forest will be seriously damaged 121 or more of the force 200 Oak trees are infected by oak wilt according to their model how many years will it take for 21 of the trees to be infected type the correct answer in the box use numerals instead of words round your answer to the nearest 10th
It will take approximately ____ years for 21 of the trees to become infected
Part c
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
Part d
Grab 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 grass of functions FNG then use your observations to describe the Relationship between the domain and range of the two functions
To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, getting that it will take 7.6 years for for 21 of the trees to become infected.
PART C
The logarithmic model is: g(x)= in x/0.4
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.
subrtract -4-(-4) the two negatives make it a + so that becomes 8 and thats for the top one the bottom is 6-2 which is 4 then divide 8 by 4 to find the slope which is 2.
