A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the chemical after t dN days is given by = -0.065N 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 600 g of the substance is present at t = 0. How much will remain after 6 days? c) What is the rate of change of the amount of the substance after 6 days? d) After how many days will half of the original 600 g of the substance remain? a) N(t) = No e -0.065t b) After 6 days, 406 g will remain. (Round to the nearest whole number as needed.) 26.39 g/day c) After 6 days, the rate of change is (Round to one decimal place as needed d) Half of the substance will remain after (Round to one decimal place as needed.) days.
A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the chemical after t dN days is given by = -0.065N 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 600 g of the substance is present at t = 0. How much will remain after 6 days? c) What is the rate of change of the amount of the substance after 6 days? d) After how many days will half of the original 600 g of the substance remain? a) N(t) = No e -0.065t b) After 6 days, 406 g will remain. (Round to the nearest whole number as needed.) 26.39 g/day c) After 6 days, the rate of change is (Round to one decimal place as needed d) Half of the substance will remain after (Round to one decimal place as needed.) days.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.3: Applications: Growth And Decay
Problem 15E
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Transcribed Image Text:A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the chemical after t
dN
days is given by = -0.065N
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 600 g of the substance is present at t= 0. How much will remain after 6 days?
c) What is the rate of change of the amount of the substance after 6 days?
d) After how many days will half of the original 600 g of the substance remain?
a) N(t) = No e
-0.065t
b) After 6 days, 406 g will remain.
(Round to the nearest whole number as needed.)
-26.39 g/day.
c) After 6 days, the rate of change is
(Round to one decimal place as needed
d) Half of the substance will remain after
(Round to one decimal place as needed.)
days
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