Question

Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f (t)=475(0.5)^t . Evaluate the function when t=3 . Round the answer to the nearest tenth

Answer 1

The initial amount (a) is 475 and the rate of decay (r) is 50% or 0.5 expressed as a decimal. When t=3, the value of the function is approximately 59.4.

Step-by-step explanation:

Solution:

The given exponential function is f(t)=475(0.5)^t. To identify the initial amount (a) and the rate of decay (r) as a percent, we can compare the equation with the general form of an exponential function y=a*b^x. Here, the initial amount (a) is 475, and the rate of decay (r) is 50% or 0.5 expressed as a decimal.

To evaluate the function when t=3, we substitute t=3 into the equation f(t)=475(0.5)^t. Using a calculator, we find f(3)=475 * (0.5)^3 = 59.375. Therefore, the value of the function when t=3 is approximately 59.4 (rounded to the nearest tenth).