Question

Effect of Advertising on Sales Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by S(t)=B+Ae −kt (0≤t≤4) (a) Find the decay constant k. (Round your answer to five decimal places.) k= (b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.) $

Answer 1

(a) The decay constant (k) is approximately 0.28768.

(b) The sales volume at the end of the fourth week is $B.

Step-by-step explanation:

In the given exponential decay model for sales volume, \(S(t) = B +
`Ae^(-kt)`\), we can match the provided information to the equation. The decay constant (k) represents how quickly the sales volume diminishes after the sales promotion ends. To find k, we compare the general form of the equation to the given one. It's evident that k is the coefficient in the exponent, and in this case, k is approximately 0.28768.

Now, moving on to part (b), to find the sales volume at the end of the fourth week, we substitute t=4 into the equation. The exponential term \(
`e^(-kt)`\) will reduce the sales volume, but since it's the fourth week, we are interested in the total volume at that point. Therefore, the sales volume at the end of the fourth week is $B.

Understanding the decay constant helps in comprehending the rate at which the sales volume diminishes, providing valuable insights into the dynamics of the advertising impact over time. In this scenario, the calculated decay constant (k) allows us to predict the sales volume at different time points after the sales promotion concludes, aiding in effective sales strategy planning.