A chemical substance has a decay rate of 8.3% per day. The rate of change of an amount N of the chemical after t days is given by = - 0.083N. dt a) Let Ng represent the amount of the substance present at t= 0. Find the exponential function that models the decay. b) Suppose that 300 g of the substance is present at t= 0. How much will remain after 5 days? c) What is the rate of change of the amount of the substance after 5 days? d) After how many days will half of the original 300 g of the substance remain? a) N(t) = b) After 5 days, g will remain. (Round to the nearest whole number as needed.) c) After 5 days, the rate of change is g/day. (Round to one decimal place as needed.) d) Half of the substance will remain after days. (Round to one decimal place as needed.)
A chemical substance has a decay rate of 8.3% per day. The rate of change of an amount N of the chemical after t days is given by = - 0.083N. dt a) Let Ng represent the amount of the substance present at t= 0. Find the exponential function that models the decay. b) Suppose that 300 g of the substance is present at t= 0. How much will remain after 5 days? c) What is the rate of change of the amount of the substance after 5 days? d) After how many days will half of the original 300 g of the substance remain? a) N(t) = b) After 5 days, g will remain. (Round to the nearest whole number as needed.) c) After 5 days, the rate of change is g/day. (Round to one decimal place as needed.) d) Half of the substance will remain after days. (Round to one decimal place as needed.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A chemical substance has a decay rate of 8.3% per day. The rate of change of an amount N of the chemical after t days is given by
NP
0.083N
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 300 g of the substance is present at t 0. How much will remain after 5 days?
c) What is the rate of change of the amount of the substance after 5 days?
d) After how many days will half of the original 300 g of the substance remain?
a) N(t) =
b) After 5 days, g will remain.
(Round to the nearest whole number as needed.)
c) After 5 days, the rate of change is g/day.
(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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