Final answer:
Using the exponential growth formula, the annual growth rate for the house's increase in value from $150,000 to $258,000 over 12 years is about 4.84%, which can be rounded to 5% to the nearest percent.
Step-by-step explanation:
To determine the annual growth rate algebraically given the sale of a house that was bought for $150,000 and sold for $258,000 after 12 years under the assumption of exponential growth, we can use the exponential growth formula:
P = P0 * e^(rt)
Where:
P is the final amount ($258,000),
P0 is the initial amount ($150,000),
r is the rate of growth,
t is the time in years (12 years), and
e is the base of the natural logarithm.
Firstly, we need to rearrange the formula to solve for the growth rate r:
r = (ln(P/P0)) / t
Plugging in the values:
r = (ln(258,000/150,000)) / 12
Next, calculate using a calculator:
r ≈ 0.0484 or 4.84%
To find the nearest percent, we round this to 5%.
Therefore, the annual growth rate is approximately 5% to the nearest percent.