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The equation of a exponential function is of the form
where
b is the base of the exponential function
If the value of b>1 -----> is a growth function
If the value of b<1 ----> is a decay function
In this problem
b=1.04
1.04 > 1
therefore
<h2>Is a growth function</h2>Part b
Determine the percentage rate of increase
we have that
b=1+r
r=b-1
r=1.04-1
r=0.04
convert to percentage
r=0.04*100
<h2>r=4%</h2>
<h3>Answer:</h3>
<u>Part A</u>:
- section A: 18
- section B: 288
<u>Part B</u>: rate of change in section B is 16 times as great
<h3>Explanation:</h3><u>Part A</u>:
The rate of change is computed as ...
... rate of change = (change in g(x)) / (change in x)
In section A, this is ...
... (change in g(x)) / (change in x) = (24 - 6)/(1 - 0) = 18
In section B, this is ...
... (change in g(x)) / (change in x) = (384 -96)/(3 -2) = 288
<u>Part B</u>:
The function, like any exponential function, increases at an increasing rate. The increase in the rate of change reflects the fact that as x increases, the rate of change of g(x) increases. (See the attachment for a graph.)