Sales of a product, under relatively stable market conditions but in the absence of promotional activities such as advertising, tend to decline at a constant yearly rate. This rate of sales decline variesconsiderably from product to product, but seems to remain the same for any particular product. The sales decline can be expressed by the function defined by the next formula.S(t) = S, e - atIn this formula S(t) is the rate of sales at timet measured in years, S, is the rate of sales at time t=0 and a is the sales decay constant. If a = 0.05 and Sn = 100,000, find the number of years it will take for salesto fall to half the initial sales......It will take about years for sales to fall to half the initial sales.(Type an integer or decimal rounded to the nearest tenth as needed.)

Answered: Image /qna-images/answer/ba1693d8-40b5-4779-aae8-c83b921547fb.jpg

Sales of a product, under relatively stable market conditions but in the absence of promotional activities such as advertising, tend to decline at a constant yearly rate. This rate of sales decline varies considerably from product to product, but seems to remain the same for any particular product. The sales decline can be expressed by the function defined by the next formula. S(t) = So e -at In this formula S(t) is the rate of sales at timet measured in years, So is the rate of sales at time t=0 and a is the sales decay constant. If a = 0.05 and Sn = 100,000, find the number of years it will take for sale to fall to half the initial sales. It will take about years for sales to fall to half the initial sales. (Type an integer or decimal rounded to the nearest tenth as needed.)

Sales of a product, under relatively stable market conditions but in the absence of promotional activities such as advertising, tend to decline at a constant yearly rate. This rate of sales decline varies considerably from product to product, but seems to remain the same for any particular product. The sales decline can be expressed by the function defined by the next formula. S(t) = So e -at In this formula S(t) is the rate of sales at timet measured in years, So is the rate of sales at time t=0 and a is the sales decay constant. If a = 0.05 and Sn = 100,000, find the number of years it will take for sale to fall to half the initial sales. It will take about years for sales to fall to half the initial sales. (Type an integer or decimal rounded to the nearest tenth as needed.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

See similar textbooks

Similar questions

Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?