Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Exponential Growth and Decay  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
So an application of exponential decay is when we are actually given a scenario about something that's increasing in quantity. For this particular problem we're going to be looking at we're dealing with the amount of a drug in a system and how it's going to decrease over time.
So we have this drug and it's decreasing according to this formula right here and we're given the amount of time that this is occurring is in hours. And what this question is asking for is, it's twopart question, first part is how much is remaining after two hours?
So this is just a function, the amount of drug is a function of time. So what we really have to do is plug in 2 in for time and see what we come up with. So this just tells us we're dealing with base of 2 is equal to 10e to the negative point 2 times 2. We plug this into our calculator and we're left with 10 times e to the .2 times 2 and that gives us around 6.7. It's a problem that doesn't tell us what our unit of measurement is if it's grams or whatever it is, so we can't have a unit, but we're left with 6.7 whatever it is.
Second part is when will there be half the original amount left in the system? For this one we actually have to do two steps. The first thing is we have to find what the original amount is, so we need to find the original amount and the first thing we need to think about is when does that occur? That occurs at time zero.
So just like we did up here where we plugged in t2 for t to find that two hours, we plug in t is equals to 0 to find the original amount, so we had 2 times 0 is 0, e to the 0 anything with a 0 is 1 so our original amount is 10. So that's our original amount.
We're now asked to figure out when we have half of that, half of 10 is 5 and so that's going to mean that we want to have left, so this is, so studying our equation 5 is equal to 10e to the .2 times t and we now have a exponential equation we need to solve. Get our exponential by itself, so we need to divide by 10 leaving us with 1/2 is equal to e to the negative point 2t. We need to get our exponent down, we have to do natural log in order to do that natural log because we already have an e here, natural log, natural log and I have natural log of 1/2is equal to .2t natural log of e.
The natural log of e becomes 1 so we can drop that out in order to finish this up divide by our coefficient on y, natural log of 1/2 over .2 is equal to 4.
We can plug this into our calculator let's figure out what our answer is, natural log of 1/2 divided by .2 and we end up with about 3 point which one is it? 3.46 and out units for time is hours.
So a application of exponential decay in this case we're dealing with concentration of drugs in one's bloodstream, but it could be a variety of different recipes or ingredients if you will and the process is always about the same.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Concept (1)
Sample Problems (8)
Need help with a problem?
Watch expert teachers solve similar problems.

Exponential Growth and Decay
Problem 1 5,443 viewsWhen Archeologists found King tuts tomb, they found a wooden stick that had 71% of its original carbon14 amount.
Using C14 dating and r = 0.00012 to figure out the age of the tomb. 
Exponential Growth and Decay
Problem 2 4,002 viewsThe amount of a drug in ones blood decreases according to A(t) = 10e^{2t}, with t in hours.
a) How much remains after 2 hours?b) When will there be half the original amount? 
Exponential Growth and Decay
Problem 3 3,021 viewsNumber of rabbits on a farm increases according to N(t) = 200e^{0.3t}, with t in months.
a) initial amountb) How many after 10 months?c) How long to triple? 
Exponential Growth and Decay
Problem 4 1,066 views 
Exponential Growth and Decay
Problem 5 857 views 
Exponential Growth and Decay
Problem 6 739 views 
Exponential Growth and Decay
Problem 7 928 views 
Exponential Growth and Decay
Problem 8 811 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete