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SSSSS [86.1K]
2 years ago
13

Please help!!!!

Mathematics
1 answer:
Irina18 [472]2 years ago
8 0

Number of trees infected after t years:

The number of trees infected after t years is given by:

f(t) = e^{0.4t}

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

f(t) = 21

Thus:

e^{0.4t} = 21

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

\ln{e^{0.4t}} = \ln{21}

0.4t = \ln{21}

t = \frac{\ln{21}}{0.4}

t = 7.6

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

f(x) = y = e^{0.4x}

e^{0.4y} = x

Again, we apply the natural logarithm to both sides of the equation, so:

\ln{e^{0.4y}} = \ln{x}

0.4y = \ln{x}

g(x) = \frac{\ln{x}}{0.4}

Thus, the logarithmic model is:

g(x) = \frac{\ln{x}}{0.4}

For an example of a problem that uses exponential functions and logarithms, you can take a look at brainly.com/question/13812761

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