Question

Write a function in terms of t that represents the situation. A $900 sound system decreases in value by 9% each year.

Answer 1

The value of the $900 sound system decreasing by 9% annually is represented by the function V(t) = 900 × (1 - 0.09)t, where t is the number of years.

Step-by-step explanation:

The situation described where a $900 sound system decreases in value by 9% each year can be represented by a function in terms of t, where t is the number of years. To model a percentage decrease in value over time, we can use an exponential decay function. Here's the formula you can use:

V(t) = P × (1 - r)t

Where:

• V(t) represents the future value of the sound system after t years
• P is the initial value of the sound system
• r is the rate of decrease (expressed as a decimal)
• t is the number of years

In this case, P is $900 and the rate of decrease r is 0.09 (9%). So the function representing the value of the sound system over time is:

V(t) = 900 × (1 - 0.09)t

This function can be used to calculate the value of the sound system after any given number of years.

Answer 2

Step-by-step explanation:

1

We are given the data:

2

The given function is an exponential decay in the form:

3

We write the function:

RESULT