Questions: Finbar invested money in a transportation 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 11 to day 15.

Finbar invested money in a transportation 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 11 to day 15.

Transcript text: Finbar invested money in a transportation 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 11 so dary 15.

Solution

Solution Steps

To find the approximate average rate of change of the function $ f(x) = 0.01(2^x) $ from day 11 to day 15, we need to calculate the values of the function at $ x = 11 $ and $ x = 15 $, and then use the formula for the average rate of change:

\[ \text{Average Rate of Change} = \frac{f(15) - f(11)}{15 - 11} \]

Step 1: Calculate $ f(11) $

To find $ f(11) $, we use the function:

\[ f(11) = 0.01(2^{11}) = 0.01 \times 2048 = 20.48 \]

Step 2: Calculate $ f(15) $

Next, we calculate $ f(15) $:

\[ f(15) = 0.01(2^{15}) = 0.01 \times 32768 = 327.68 \]

Step 3: Calculate the Average Rate of Change

Now, we find the average rate of change from day 11 to day 15 using the formula:

\[ \text{Average Rate of Change} = \frac{f(15) - f(11)}{15 - 11} = \frac{327.68 - 20.48}{4} = \frac{307.2}{4} = 76.8 \]