Question

the graph below shows the growth of two retirement accounts. the function $s_{25}(t)$ shows the balance in thousands of dollars of someone who began investing at age 25, and $s_{35}(t)$ shows the balance of someone who began investing at age 35. compare the average rate of change in both accounts from age 50 to age 60. then complete the sentence below: 8. “from 50 to 60 years old, the person who started investing at age 25 will earn ______ more on average than a person who started investing at age 35.” mark only one oval. $13.96 thousand per year $17.63 thousand per year $31.59 thousand per year $49.22 thousand per year

Explanation:

Step1: Calculate average rate of change for \(S_{25}(t)\)

The formula for average rate of change is \(\frac{f(b)-f(a)}{b - a}\). For \(S_{25}(t)\), \(a = 50\), \(f(a)=311.0\), \(b = 60\), \(f(b)=626.9\).

$$ \frac{626.9 - 311.0}{60 - 50}=\frac{315.9}{10}=31.59 $$

Step2: Calculate average rate of change for \(S_{35}(t)\)

For \(S_{35}(t)\), \(a = 50\), \(f(a)=134.7\), \(b = 60\), \(f(b)=311.0\).

$$ \frac{311.0 - 134.7}{60 - 50}=\frac{176.3}{10}=17.63 $$

Step3: Find the difference

Subtract the average rate of change of \(S_{35}(t)\) from that of \(S_{25}(t)\)

$$ 31.59-17.63 = 13.96 $$

Answer:

\(\$13.96\) thousand per year