Question

If anybody sees this can they help me out

The trees in a forest are being cut down at a monthly rate of 3.2%. This situation can be modeled by an exponentia function. The forest contained 5,500 trees when cutting began. Which function can be used to find the number of trees in the forest at the end of m months?

A) t(m) -5,500(0.032)m
B) t(m) - 5,500(1.968)m
C) t(m) -5,500(1.032)m
D) t(m) -5,500(0.968)m

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Answer 1

B

Explanation:

The function that models the situation is an exponential decay function of the form:

t(m) = a(1 - r)^m

where:

t(m) is the number of trees after m months

a is the initial number of trees (5,500 in this case)

r is the monthly rate of decrease (3.2% or 0.032 as a decimal)

Substituting the values given in the options, we get:

A) t(m) = 5,500(0.032)^m

B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m

C) t(m) = 5,500(1.032)^m

D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m

Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.

Answer 2

Answer: The formula for exponential decay is given by:

t(m) = a(1-r)^m

where

a = initial value

r = decay rate

Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:

t(m) = 5,500(1 - 0.032)^m

t(m) = 5,500(0.968)^m

Therefore, the answer is (D) t(m) = 5,500(0.968)^m.

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