Answer:
A) R = 27.687
B) t = 8 days
Step-by-step explanation:
(English question:
Suppose that the percentage R of people who respond to the advertisement of a new product in a newspaper and who buy it after t days, is given by the following formula: R = 50-100 * e ^ -0'3 * t A) What percentage of people have responded and bought after 5 days? B) How many days must elapse before the percentage that has responded and bought is 40%?)
A) To find the percentage of people that responded and bought after 5 days, we just need to use the value of t = 5 in the equation of R:
R = 50 - 100*e^(-0.3*5) = 50 - 22.313 = 27.687
B) To find how many days must elapse for the percentage to be 40%, we need to use the value of R = 40 and then find the value of t:
40 = 50 - 100*e^(-0.3*t)
-100*e^(-0.3*t) = -10
e^(-0.3*t) = 0.1
Using ln (natural logarithm) in both sides:
ln(e^(-0.3*t)) = ln(0.1)
-0.3*t = -2.3026
t = 7.6753 days
So after 8 days the percentage will be higher than 40%
