Terrance invested money in a technology stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 3 to day 8.

Question

0.496
2.016
2.48
5

Answer 1

To find the average rate of change of the function \( f(x) = 0.01(2)^x \) from day 3 to day 8, we can use the formula for the average rate of change over an interval \([a, b]\):

\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]

Here, we have \( a = 3 \) and \( b = 8 \).

First, we calculate \( f(3) \):

\[ f(3) = 0.01(2)^3 = 0.01 \times 8 = 0.08 \]

Next, we calculate \( f(8) \):

\[ f(8) = 0.01(2)^8 = 0.01 \times 256 = 2.56 \]

Now we substitute these values into the average rate of change formula:

\[ \text{Average Rate of Change} = \frac{f(8) - f(3)}{8 - 3} = \frac{2.56 - 0.08}{5} = \frac{2.48}{5} = 0.496 \]

Thus, the approximate average rate of change from day 3 to day 8 is \( \boxed{0.496} \).