Question

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation mc010-1. Jpg to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced? 6. 1 6. 6 7. 2 23. 1.

Answer 1

With no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

What is an exponential function?

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

A type of plant is introduced into an ecosystem and quickly begins to take over.

A scientist counts the number of plants after m months and develops the equation to model the situation, which is given as,

$p(m)=19.3(1089)^m$

Most recently, the scientist counted 138 plants.

$138=19.3(1089)^m\\(1089)^m=7.15$

Taking log both sides of the equation,

$\log(1.089)^m=\log7.15\\m\log(1.089)=\log(7.15)\\m=\dfrac{\log7.15}{\log(1.089)}\\m\approx23.1$

Thus, with no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

Learn more about the exponential function here;

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