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?
A. 6.1
B.6.6
C.7.2
D.23.1

Answer 1

Answer:

D. 23.1 is the correct answer

Step-by-step explanation:

We are given that,

The model representing the number of plants after 'm' months is given by,

$P(m)=19.3(1.089)^m$.

Now, the number of plants currently counted are 138.

It is required to find the number of months passed.

So, we have,

$138=19.3(1.089)^m$

i.e. $(1.089)^m=\frac{138}{19.3}$

i.e. $(1.089)^m=7.15$

i.e. $m\log (1.089)=\log 7.15$

i.e. $m\times 0.037=0.854$

i.e. $m=\frac{0.854}{0.037}$

i.e. m = 23.1

Thus, the number of months passed are 23.1.

So, option D is correct.

Answer 2

Answer:

the answer is D.

Step-by-step explanation:

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