Question

directions: use this information to answer parts a and b. the value of a textbook is $53 and depreciates at a rate of 15% per year for t years. part a find an exponential decay function to model the situation. enter the correct expression in the box, using t to represent the time in years. hide hints the exponential decay model for this situation is of the form v(t)=a(1 - r)^t. v(t)=53×0.85^t

Explanation:

Step1: Identify the exponential decay formula

The general formula for exponential decay is \( v(t) = a(1 - r)^t \), where \( a \) is the initial value, \( r \) is the rate of decay (in decimal form), and \( t \) is time in years.

Step2: Determine the values of \( a \) and \( r \)

• The initial value of the textbook \( a = 53 \) (in dollars).
• The depreciation rate is \( 15\% \), which in decimal form is \( r = 0.15 \).

Step3: Substitute \( a \) and \( r \) into the formula

Substitute \( a = 53 \) and \( r = 0.15 \) into \( v(t) = a(1 - r)^t \). First, calculate \( 1 - r \): \( 1 - 0.15 = 0.85 \). Then the function becomes \( v(t) = 53 \times 0.85^t \).

Answer:

\( v(t) = 53 \times 0.85^t \)