Question

A river has a population of 700 salmon. Due to overfishing, this population is currently declining at a rate of 5% per year. Use this sequence to find the population over the next

five years. Round to the nearest whole number.



Please Help Me

Answer 1

f(1)=665, f(2)=632, f(3)=600, f(4)=570, f(5)=542

Step-by-step explanation

Acellus wants you to use Geometric Recursive to solve this formula. I would recommend rounding your answers last.

f(n)=f(n-1)x-0.05f(n-1)

your first f(n) value is your starting population, f(0)=700, plug this into your equation for the f(1) value.

f(1)=(700)x-0.05(700)

answer/next value 665

Repeat the previous step but with the answer as your new value for the rest of the equations below

f(2)=(665)x-0.05(655)

answer/next value 632

f(3)=(632)x-0.05(632)

answer/next value 600

f(4)=(600)x-0.05(600)

answer/next value 570

f(5)=(570)x-0.05(570)

final answer 542

Although this was brief, I hope it was helpful to you.

Answer 2

665, 632, 600, 570, 542

Explanation:

When the amount of decline is a percentage of the declining population, the sequence is described by an exponential function. The general form of the function is ...

population = (initial value)×(1 -rate of change)^t

Using the given numbers, the function can be written ...

f(t) = 700×0.95^t

The attached table shows the function values for the values of t given in your table.

_____

Using a suitable calculator, evaluation of the function is straightforward. For example, f(5) = 700(0.95^5) = 700(0.77378) ≈ 541.65 ≈ 542.

It is generally best to save the rounding step until the end, rather than computing each value from the previous rounded value. If you do these calculations in a spreadsheet, you can use cell formatting to show the result as an integer. You do not need the "round" function as part of the formula.