Question

Write a function in terms of t that represents the situation.

A $900 sound system decreases in value by 9% each year.
y=

Answer 1

y = 900(0.91^t)

Explanation:

You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.

Exponential function

When the amount of change is proportional to the amount, the amount is described by an exponential function:

y = ab^x

where 'a' is the initial value, and 'b' is the "growth factor."

Application

Here, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:

b = 1 +(-9%) = 1 -0.09 = 0.91

The initial value is given as ...

a = 900

So the function you want is ...

y = 900(0.91^t)

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Additional comment

The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.