Answer to Question #215164 in Calculus for Akhona Klanisi

Question

Questions 4 and 5 are based on the following information: The daily rate of sales of a product (in units per day) is approximated by the exponential function

S(t) = 1800 + 1500e^−0,3t+1,5

with t the number of days it has been on the market.

Question  4

After 20 days the rate of sales of the product is approximately

 

1.      37.

2.      108.

3.      1 817.

4.      1 783.

 

Question   5

After how many days, rounded to a whole number, will the rate of sale be 2 000 units per day?

 

1.      4

2.      5

3.      11

4.      12

Answer 1

Question 4

$t=20\\ S(t)=S(20)=1800 + 1500e^{−0.3t+1.5}\\ S(20)=1800 + 1500e^{−0.3*20+1.5}\\ S(20)=1800 + 17\\ S(20)=1817$

Option 3 is correct

Question 5

$S(t) = 1800 + 1500e^{−0.3t+1.5}\\ 2 000=1800 + 1500e^{−0.3t+1.5}\\ 1800+1500e^{-0.3t+1.5}-1800=2000-1800\\ 1500e^{-0.3t+1.5}=200\\ e^{-0.3t+1.5}=\frac{2}{15}\\ t=\frac{-\ln \left(\frac{2}{15}\right)+1.5}{0.3}\\ t=11.7=12$

Option 4 is correct