Question

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.

Answer 1

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

$\rm y = 40(1 - 0.01)^t\\\\y = 40(0.99)^t$

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.

brainly.com/question/5497425

#SPH1