Question

The value of a rare baseball card is modeled by the function V(t)=2.25(1.32)^t where T is the number of years by what percent rate is the value of the car increasing per year

Answer 1

The percentage rate at which the value of the baseball card is increasing per year can be found by calculating the derivative of the function V(t). The derivative of V(t) with respect to t represents the rate of change of the function, which in this case, is the rate at which the value of the baseball card is increasing.

Step-by-step explanation:

The percentage rate at which the value of the baseball card is increasing per year can be found by calculating the derivative of the function V(t). The derivative of V(t) with respect to t represents the rate of change of the function, which in this case, is the rate at which the value of the baseball card is increasing.

To find the derivative, we can use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = ax^n, then the derivative of f(x) with respect to x is f'(x) = nax^(n-1).

In this case, the function V(t) = 2.25(1.32)^t can be rewritten as V(t) = 2.25 * (1.32^t). Using the power rule, we can find the derivative of V(t) as V'(t) = 2.25 * ln(1.32) * (1.32^t). This derivative represents the rate at which the value of the baseball card is increasing per year.