Answer:
1. Forest B
2. Forest A
3. 19
4. Forest B
5. 17.34
Step-by-step explanation:
The exponential function has the form
f(t) = a(1 + r)^t
Where a is the initial value and r is the growth rate.
The equation for each forest can be written as
A(t) = 107(1.015)^t
A(t) = 107(1 + 0.015)^t
B(t) = 88(1.025)^t
B(t) = 88(1 + 0.025)^t
Therefore, for each forest, we get:
Forest A
The initial number of trees: 107
Growth rate: 0.015 = 1.5%
Forest B
Initial number of trees: 88
Growth rate: 0.025 = 2.5%
Since 2.5% is greater than 1.5%, Forest B has a faster rate
Since 107 is greater than 88, Forest A has a greater number of trees initially
The difference between the initial amount of three is equal to 19 because
107 - 88 = 19
To know the number of trees in each forest after 30 years, we need to replace t = 30 on each equation, so
A(t) = 107(1.015)^30
A(t) = 167.25
B(t) = 88(1.025)^30
B(t) = 184.59
Therefore, forest B will have more trees after 30 years and the difference between the number of trees will be
184.59 - 167.25 = 17.34
So, the answers are:
1. Forest B
2. Forest A
3. 19
4. Forest B
5. 17.34