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ahrayia [7]
2 years ago
3

13. In California’s gold rush, some towns grew exponentially. If a certain town started with 45 people and had 360 people 15 mon

ths later, what is the growth rate? (r can also be per month instead of per year)
Advanced Placement (AP)
1 answer:
maxonik [38]2 years ago
5 0

Answer:

The growth rate of the town is approximately 0.212 per month.

Explanation:

The exponential model is defined by the following formula:

n = n_{o}\cdot e^{r\cdot t} (1)

Where:

n_{o} - Initial population, dimensionless.

r - Growth rate, measured in \frac{1}{mo}.

t - Time, measured in months.

n - Current population, dimensionless.

From (1), we clear the growth rate as follows:

\frac{n}{n_{o}} = e^{r\cdot t}

r = \frac{1}{t}\cdot \ln \frac{n}{n_{o}} (2)

If we know that n_{o} = 45, n = 360 and t = 15\,mo, then the growth rate is:

r = \left(\frac{1}{15\,mo}\right)\cdot \ln \frac{360}{15}

r \approx 0.212\,\frac{1}{mo}

The growth rate of the town is approximately 0.212 per month.

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