the function a=275(9/10)^t represents the area A (in square miles) of a coral reef after t years. By what percentage does the area of coral reef decrease each year?

Answer 1

It decreases by 10%. We can know this by looking at the function and seeing the 9/10. 9/10 is the same as 0.9, or 90%, which is 100%-10%. After one year, putting a 1 in place of t gives us a = 275(9/10)¹, or a = 275(9/10), or a = 275*0.9. This results in 247.5, which is the same as 275 - 27.5, or subtracting 10%. This is how you can check your answer. If you keep doing this subtraction of 10%, you will see the results are consistent with the function.

Year 1: 247.5

Year 2: 222.75 (or 247.5 - 10%, aka 24.75)

and so on.