A population numbers 20,000 organisms initially and grows by each year.
Suppose represents population, and the number of years of growth. An exponential model for the
population can be written in the form where

Ask by Bolton Gibson. in the United States

Nov 12,2024

Question

A population numbers 20,000 organisms initially and grows by each year.
Suppose represents population, and the number of years of growth. An exponential model for the
population can be written in the form where

Ask by Bolton Gibson. in the United States

Nov 12,2024

UpStudy AI · Accepted Answer

To model the population growth of the organisms using an exponential function, we can use the formula:

$$
P = a \cdot b^t
$$

where:
- $$ P $$ is the population at time $$ t $$,
- $$ a $$ is the initial population,
- $$ b $$ is the growth factor,
- $$ t $$ is the time in years.

Given that the initial population $$ a $$ is 20,000 organisms, we have:

$$
a = 20000
$$

The population grows by $$ 13.2\% $$ each year. This means that the growth factor $$ b $$ can be calculated as follows:

$$
b = 1 + \text{growth rate} = 1 + 0.132 = 1.132
$$

Now we can substitute $$ a $$ and $$ b $$ into the exponential model:

$$
P = 20000 \cdot (1.132)^t
$$

Thus, the exponential model for the population is:

$$
P = 20000 \cdot (1.132)^t
$$
The exponential model for the population is $$ P = 20000 \cdot (1.132)^t $$.

A population numbers 20,000 organisms initially and grows by each year.
Suppose represents population, and the number of years of growth. An exponential model for the
population can be written in the form where

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A population numbers 20,000 organisms initially and grows by each year. Suppose represents population, and the number of years of growth. An exponential model for the population can be written in the form where

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A population numbers 20,000 organisms initially and grows by each year.
Suppose represents population, and the number of years of growth. An exponential model for the
population can be written in the form where