Question

A school of fish has the population of 200. The population is decreasing at a rate of 5% a year how can you write in exponential decay function to find the quarterly decay rate

Answer 1

Answer:

$P=200(0.9875)^n$

Step-by-step explanation:

Initial population of fish = 200

Decay rate by which population is decreasing = 5% per year

Number of quarters in a year = 4

Rate of decay in a quarter = $\frac{5}{4}$ = 1.25%

Formula for the exponential decay in the population is,

$P=P_0(1-\frac{r}{100})^n$

Here, P = Final population

P₀ = Initial population

r = Rate of decay per quarter

n = Number of quarters for the total decay

By substituting these values in the formula,

$P=200(1-\frac{1.25}{100})^n$

$P=200(1-0.0125)^n$

$P=200(0.9875)^n$

Answer 2

The quarterly decay rate is given by $\rm P = 200(0.9875)^n$  and this can be determined by using the exponential decay function.

Given :

• A school of fish has a population of 200.
• The population is decreasing at a rate of 5% a year.

The formula of exponential decay is given by the equation:

$\rm P = P_0\left(1- \dfrac{r}{100}\right)^n$      ----- (1)

where n is the number of quarters for total decay, r is the rate of decay per quarter, $\rm P_0$ is the initial population and P is the final population.

Now, put the values of known terms in the equation (1).

$\rm P = 200\left(1-\dfrac{1.25}{100}\right )^n$

$\rm P = 200(1-0.0125)^n$

$\rm P = 200(0.9875)^n$

The quarterly decay rate is given by $\rm P = 200(0.9875)^n$ .

For more information, refer to the link given below:

https://brainly.com/question/19601887