Answer to Question #215164 in Calculus for Akhona Klanisi

Question #215164

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


1
Expert's answer
2021-07-12T16:10:04-0400

Question 4

t=20S(t)=S(20)=1800+1500e0.3t+1.5S(20)=1800+1500e0.320+1.5S(20)=1800+17S(20)=1817t=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+1500e0.3t+1.52000=1800+1500e0.3t+1.51800+1500e0.3t+1.51800=200018001500e0.3t+1.5=200e0.3t+1.5=215t=ln(215)+1.50.3t=11.7=12S(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


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment