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 \\(p(m) = 19.3(1.089)^m\\) 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

Explanation:

Set up the exponential equation

$$ 19.3(1.089)^m = 138 $$

Isolate the exponential term

$$ (1.089)^m = \frac{138}{19.3} \approx 7.15026 $$

Solve for m using logarithms

$$ m = \frac{\ln(7.15026)}{\ln(1.089)} \approx \frac{1.9671}{0.08526} \approx 23.07 $$

Answer:

• 6.1
• 6.6
• 7.2
• 23.1 (Correct answer)