## help_people one year ago @skullpatrol

1. help_people

The number of subscribers y to a magazine after t years is shown by the equation below: y = 95(0.75)t Which conclusion is correct about the number of subscribers to the magazine? It increased by 25% every year. It decreased by 25% every year. It increased by 75% every year. It decreased by 75% every year.

2. help_people

i bleive this one is d

3. mathstudent55

Is t an exponent?

4. help_people

yes t is an expontnet @mathstudent55

5. help_people

ok @skullpatrol jstu to clarify d is wrong?

6. help_people

based on what you are showing me it is increasing

7. skullpatrol

yes

8. skullpatrol

$$\Huge y = 95(0.75)^t$$

9. skullpatrol

is that^ the equation?

10. skullpatrol
11. help_people

yes @skullpatrol

12. mathstudent55

Calculate the function for t = 0. $$y = 95(0.75)^0 = 95 \times 1 = 95$$ At t = 0, the initial numbers of subscribers is 95. Now let's calculate y for t = 1, at the end of 1 year. $$y = 95(0.75)^1 = 95 \times 0.75 = 71.25$$ At t = 1, the end of the first year, the number of subscribers is 71.25. Now calculate the percent decrease from 95 to 71.25: $$percent~change = \dfrac{71.25 - 95}{95} \times 100 = -25\%$$ A negative percent change is a decrease. The decrease is 25% per year.

13. mathstudent55

This problem can be solved without graphs or any calculations. All you need to do is to compare the equation you were given with the growth/decay formula: $$F = P(1 + r)^t$$ where F = future amount, P = present amount r = rate of increase or decrease t = time in years If r is a rate of increase, then r is positive. A negative r means a rate of decrease. Now let's compare this formula with your given equation. $$y = 95(0.75)^t$$ must fit into $$F = P(1 + r)^t$$, then you get $$y = 95[1 + (-0.25)]^t$$ Notice that to have 1 + r in the parentheses, you need to write 0.75 as 1 + (-0.25). This clearly shows that the rate is 25% decrease annually.

14. help_people

thank you