A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical after t dN days is given by = -0.069N. dt a) Let No represent the amount of the substance present at t= 0. Find the exponential function that models the decay b) Suppose that 700 g of the substance is present at t= 0. How much will remain after 2 days? c) What is the rate of change of the amount of the substance after 2 days? d) After how many days will half of the original 700 g of the substance remain? a) N(t) = b) After 2 days, g will remain.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CT: Chapter Test
Problem 11CT
Question
A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical after t
dN
days is given by = -0.069N.
dt
a) Let No represent the amount of the substance present at t = 0. Find the exponential function that models the decay.
b) Suppose that 700 g of the substance is present at t = 0. How much will remain after 2 days?
c) What is the rate of change of the amount of the substance after 2 days?
d) After how many days will half of the original 700 g of the substance remain?
a) N(t) =
b) After 2 days,g will remain.
(Round to the nearest whole number as needed.)
g/day.
c) After 2 days, the rate of change is
(Round to one decimal place as needed.)
d) Half of the substance will remain after days.
(Round to one decimal place as needed.)
Transcribed Image Text:A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical after t dN days is given by = -0.069N. dt a) Let No represent the amount of the substance present at t = 0. Find the exponential function that models the decay. b) Suppose that 700 g of the substance is present at t = 0. How much will remain after 2 days? c) What is the rate of change of the amount of the substance after 2 days? d) After how many days will half of the original 700 g of the substance remain? a) N(t) = b) After 2 days,g will remain. (Round to the nearest whole number as needed.) g/day. c) After 2 days, the rate of change is (Round to one decimal place as needed.) d) Half of the substance will remain after days. (Round to one decimal place as needed.)
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