A house purchased 5 years ago for $$ \$ 100,000 $$ was just sold for $$ \$ 135,000 $$. Assuming exponential growth, approximate the annual growth rate, to the nearest percent.

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To determine the annual growth rate for the house price assuming exponential growth, we can use the continuous growth formula:

$$
P = P_0 \times e^{rt}
$$

Where:
- $$ P $$ is the final amount (\$135,000)
- $$ P_0 $$ is the initial amount (\$100,000)
- $$ r $$ is the annual growth rate
- $$ t $$ is the time in years (5 years)

Plugging in the known values:

$$
135,000 = 100,000 \times e^{5r}
$$

First, divide both sides by 100,000:

$$
1.35 = e^{5r}
$$

Next, take the natural logarithm of both sides to solve for $$ r $$:

$$
\ln(1.35) = 5r
$$

$$
r = \frac{\ln(1.35)}{5} \approx \frac{0.3001}{5} \approx 0.0600 \text{ or } 6.00\%
$$

Therefore, the approximate annual growth rate is **6%**.

**Answer:** 6\%
The annual growth rate is approximately 6%.

A house purchased 5 years ago for was
just sold for . Assuming exponential
growth, approximate the annual growth rate, to the
nearest percent.

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A house purchased 5 years ago for was just sold for . Assuming exponential growth, approximate the annual growth rate, to the nearest percent.