Final answer:
To find the value of a book after 8 years with an initial value of $58 and a decay rate of 7% per year, use the exponential decay formula V(t) = V₀ * e^-(r*t). Replace V₀ with $58, r with 0.07, and t with 8, then calculate V(8) = 58 * e^-0.56.
Step-by-step explanation:
Calculating the Value of a Book Over Time Using Exponential Decay
The problem involves using an exponential decay function to calculate the value of a book that was initially worth $58 and decreases in value by 7% each year. The exponential function to model the decay in value is given by V(t) = V₀ * e-(r*t), where V(t) is the value at time t, V₀ is the initial value, e is the base of the natural logarithm, r is the decay rate, and t is the time in years. For the given problem, the initial value V₀ is $58, the decay rate r is 0.07 (7% expressed as a decimal), and we are looking to find the value after 8 years (t = 8).
Using the formula, we get V(8) = 58 * e-(0.07*8). When calculated, this gives us the remaining value of the book after 8 years.
To find the exact value, we calculate: V(8) = 58 * e-(0.07*8) = 58 * e-0.56. Hence, the remaining value of the book can be derived using a calculator with an exponential function capability.