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A chemical substance has a decay rate of 8.7% per day. The rate of change of an amount N of the chemical after t days is given by = - 0.087N 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 400 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 400 g of the substance remain? .... -0.087t a) N(t) = No e b) After 2 days, 336 g will remain. (Round to the nearest whole number as needed.) c) After 2 days, the rate of change is -29.2 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 8.7% per day. The rate of change of an amount N of the chemical after t days is given by = - 0.087N 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 400 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 400 g of the substance remain? .... -0.087t a) N(t) = No e b) After 2 days, 336 g will remain. (Round to the nearest whole number as needed.) c) After 2 days, the rate of change is -29.2 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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 39E
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dN = - 0.087N. dt A chemical substance has a decay rate of 8.7% per day. The rate of change of an amount N of the chemical after t days is given by a) Let No represent the amount of the substance present at t= 0. Find the exponential function that models the decay. b) Suppose that 400 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 400 g of the substance remain? 0.087t a) N(t) = No e b) After 2 days, 336 g will remain. (Round to the nearest whole number as needed.) c) After 2 days, the rate of change is - 29.2 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.)
Transcribed Image Text:dN = - 0.087N. dt A chemical substance has a decay rate of 8.7% per day. The rate of change of an amount N of the chemical after t days is given by a) Let No represent the amount of the substance present at t= 0. Find the exponential function that models the decay. b) Suppose that 400 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 400 g of the substance remain? 0.087t a) N(t) = No e b) After 2 days, 336 g will remain. (Round to the nearest whole number as needed.) c) After 2 days, the rate of change is - 29.2 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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