point(s) possible Submit quiz The sales of a new high-tech item (in thousands) are given by the following function, where t represents time in years. Find the rate of change of sales at each time. \[ S(t)=107-90 e^{-0.4 t} \] (a) After 1 year. (b) After 5 years. (c) What is happening to the rate of change of sales as time goes on? (d) Does the rate of change of sales ever equal zero? (a) The rate of change after 1 year is thousand items per year. (Round to three decimal places as needed.) (b) The rate of change after 5 years is thousand items per year. (Round to three decimal places as needed.) (c) What is happening to the rate of change of sales as time goes on? A. First it increases, then it decreases. B. It always increases. C. It always decreases. D. First it decreases, then it increases. (d) Does the rate of change of sales ever equal zero? Yes Submit quiz

Step 1 ：Find the derivative of the function S(t) = 107 - 90e^(-0.4t) using the chain rule. The derivative is S'(t) = 36e^(-0.4t).

Step 2 ：Calculate the rate of change after 1 year by substituting t=1 into the derivative. The rate of change is S'(1) = 36e^(-0.4*1) = \(\boxed{27.392}\) thousand items per year.

Step 3 ：Calculate the rate of change after 5 years by substituting t=5 into the derivative. The rate of change is S'(5) = 36e^(-0.4*5) = \(\boxed{5.305}\) thousand items per year.

Step 4 ：The rate of change of sales as time goes on is given by the derivative S'(t) = 36e^(-0.4t). As t increases, the value of e^(-0.4t) decreases, which means the overall value of S'(t) decreases. So, the rate of change of sales always decreases.

Step 5 ：The rate of change of sales equals zero when S'(t) = 0. However, since S'(t) = 36e^(-0.4t), and e^(-0.4t) is always positive for any real number t, S'(t) can never be zero. So, the rate of change of sales never equals zero.