After the end of an advertising campaign, the sales of a product is given by S=900,000e 0.2t where S is weekly sales in dollars and t is the number of weeks since the end of the campaign. (a) Find the rate of change of S (that is, the rate of sales decay). dS dt = (b) From looking at the function and its derivative, explain how you know sales are decreasing. The given function is an exponential ---Select--- ✓ model. Additionally, the derivative of the given function is always ---Select--- Pollution levels in a lake have been modeled by the equation x = 0.05 +0.18e-0.38t where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of change of x with respect to time? x'(t) = With U.S. Department of Health and Human Services data from 2002 and projected to 2024, the total public expenditures for health care H can be modeled by H = 1,500 0.053t where t is the number of years past 2000 and H is in billions of dollars. If this model is accurate, at what rate (in billions of dollars per year) will health care expenditures change in 2021? (Round your answer to one decimal place.) $ billion/year
After the end of an advertising campaign, the sales of a product is given by S=900,000e 0.2t where S is weekly sales in dollars and t is the number of weeks since the end of the campaign. (a) Find the rate of change of S (that is, the rate of sales decay). dS dt = (b) From looking at the function and its derivative, explain how you know sales are decreasing. The given function is an exponential ---Select--- ✓ model. Additionally, the derivative of the given function is always ---Select--- Pollution levels in a lake have been modeled by the equation x = 0.05 +0.18e-0.38t where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of change of x with respect to time? x'(t) = With U.S. Department of Health and Human Services data from 2002 and projected to 2024, the total public expenditures for health care H can be modeled by H = 1,500 0.053t where t is the number of years past 2000 and H is in billions of dollars. If this model is accurate, at what rate (in billions of dollars per year) will health care expenditures change in 2021? (Round your answer to one decimal place.) $ billion/year
Chapter1: Introducing The Economic Way Of Thinking
Section1.A: Applying Graphics To Economics
Problem 20SQ
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Transcribed Image Text:After the end of an advertising campaign, the sales of a product is given by
S=900,000e 0.2t
where S is weekly sales in dollars and t is the number of weeks since the end of the campaign.
(a) Find the rate of change of S (that is, the rate of sales decay).
dS
dt
=
(b) From looking at the function and its derivative, explain how you know sales are decreasing.
The given function is an exponential ---Select--- ✓ model. Additionally, the derivative of the given
function is always ---Select---
Pollution levels in a lake have been modeled by the equation
x = 0.05 +0.18e-0.38t
where x is the volume of pollutants (in cubic kilometers) and t is the time (in years). What is the rate of
change of x with respect to time?
x'(t) =
With U.S. Department of Health and Human Services data from 2002 and projected to 2024, the total
public expenditures for health care H can be modeled by
H = 1,500 0.053t
where t is the number of years past 2000 and H is in billions of dollars. If this model is accurate, at what
rate (in billions of dollars per year) will health care expenditures change in 2021? (Round your answer to
one decimal place.)
$
billion/year
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