A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years.

Write the particular solution to the differential equation which describes the number of fish over time.

Question

13-06-2022
Mathematics

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A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years.

Write the particular solution to the differential equation which describes the number of fish over time.

Respuesta :

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jainveenamrata jainveenamrata · Answer 1 · 2022-06-16T08:05:28+02:00

The particular solution to the differential equation which describes the number of fish over time will be y = 40(0.99)^t.

What is an exponent?

Consider the function:

y = a (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years.

Let y be the number of fish over time (t).

Then we have

[tex]\rm y = 40(1 - 0.01)^t\\\\y = 40(0.99)^t[/tex]

Then the particular solution to the differential equation which describes the number of fish over time will be y = 40(0.99)^t.

More about the exponent link is given below.

https://brainly.com/question/5497425

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A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years. Write the particular solution to the differential equation which describes the number of fish over time.

Respuesta :

What is an exponent?

Otras preguntas

A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years.

Write the particular solution to the differential equation which describes the number of fish over time.