Chapter 6.4, Problem 61E

a.

To determine

To write the function that represents the basal areas of the trees after $t$ years.

Answer to Problem 61E

  $A_A=120{(1.1)}^t$ , $A_B=154{(1.06)}^t$

Explanation of Solution

Given:

The following table shows the basal areas (in square inches) of Tree A over time.

  

Calculation:

Using the exponential growth function $y=a{(1+r)}^t$

For Tree A:

From the table $a=120(\text{initial value)}$ and $1+r=1.1$

Therefore the model for tree A is $A_A=120{(1.1)}^t$

For Tree B:

From the table $a=154(\text{initial value)}$ and $1+r=1.06$

Therefore the model for tree B is $A_B=154{(1.06)}^t$

b.

To determine

To graph the two functions in the same coordinate plane and compare the areas.

Answer to Problem 61E

The basal area of tree A grows at faster rate at $10\%$ per year than the basal area of tree B which grows at a rate of $6\%$ per year.

Explanation of Solution

Given:

The following table shows the basal areas (in square inches) of Tree A over time.

  

Calculation:

  

The basal area of tree A grows at faster rate at $10\%$ per year than the basal area of tree B which grows at a rate of $6\%$ per year.