a person invested $3,500 in an account growing at a rate allowing the money to double every 15 years. how…

Explanation:

Step1: Identify the growth - pattern

The money doubles every 15 years. The initial investment is $P = 3500$. When it doubles, the amount $A=7000$.

Step2: Analyze the additional growth

We want to reach $A = 7700$ from $7000$. First, find the ratio of growth: $\frac{7700}{7000}=1.1$. Let the time for the money to grow from $7000$ to $7700$ be $t$ years. Assuming continuous - compounding (or a constant growth rate model), if the money doubles in 15 years, the growth formula can be written in terms of a general exponential growth model. But we can also use a simple proportion. Since the growth is assumed to be linear in terms of the factor of growth over short intervals (relative to the 15 - year doubling period). The growth from $7000$ to $7700$ is a 10% growth. If the money doubles (100% growth) in 15 years, for a 10% growth, we set up the proportion $\frac{t}{15}=\frac{0.1}{1}$.

Step3: Solve for $t$

Cross - multiply the proportion: $t = 15\times0.1=1.5$ years. The total time to reach $7700$ from the start is the time to double ($15$ years) plus the additional time to grow from $7000$ to $7700$. So the total time $T=15 + 1.5=16.5$ years.

Answer:

$16.5$