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### Course: Precalculus (Eureka Math/EngageNY) > Unit 3

Lesson 15: Topic C: Lessons 20-21: Inverse relationship of exponentials and logarithms- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: graphs
- Relationship between exponentials & logarithms: tables
- Relationship between exponentials & logarithms
- Half-life and carbon dating
- Exponential model word problem: medication dissolve
- Exponential model word problem: bacteria growth
- Exponential model word problems

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# Exponential model word problem: bacteria growth

Sal evaluates an exponential function at a specific value in order to answer a question about an exponential model.

## Want to join the conversation?

- Do bacteria actually produce future generations exponentially like it is described in the problem?(15 votes)
- I think they do, pretty much like any other species. However, in case of bacteria cumulative outcome of this reproduction is very substantial and visible, as (under favourable conditions) they produce subsequent generations very frequently. Much more frequently than previous generations fade away.(15 votes)

- Wondering why this video is included in the Algebra II logarithms section. The problem doesn't require the use of logarithms.(12 votes)
- You're right that logs were not needed. This is because you were given a value for t. If the problem had asked you to find "t" when b(t) = 10,240, then you would have needed logarithms.

This is likely why the video is in the logarithm section.(4 votes)

- Shouldn't you divide by 120 for the last step?(5 votes)
- 120 is the amount of time given, so you don't divide by 120.(5 votes)

- Hi Thank you for the awesome videos.

I just have one question. When rounding to the nearest thousandth and hundredth, how do i know when to round up?(4 votes)- Did you check responses to your earlier posted questions? I posted an answer to this over 5 hours ago. FYI - There are also lessons on rounding and rounding decimals in KA that might help you.(4 votes)

- how to solve this question sir?

The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day?(3 votes)- If it doubles every 2 hours, you have a exponential function y=ab^x, a initial value b is base. So you have y=120 (2)^x. 1 day has 12 2 hour periods and 1/2 of a day has 6 two hour periods, so substitute for with x=18.(6 votes)

- At0:55where did 2^5 come from?(3 votes)
- Since 2^10 is the same as 2^5 * 2^5 he was just breaking it down into something easier to calculate to verify that he had the right answer for 2^10 before working the rest of the equation.(5 votes)

- Can someone explain how the -25 on the last line was derived? Got lost on that part.

100-30*e^(-0.04t)=80

-30*e^(-0.04t)=-20

e^(-0.04t)=2/3

-0.04t = ln(2/3)

t = -25*ln(2/3)

From Quiz.

Thank you.(2 votes)- We multiplied both sides by -25. -25·(-0.04)=1, so we just have t on the left-hand side.(5 votes)

- 10^d/2 = 16,000

to

d/2 =log(16,000)

shouldn't it be division insted of multiplication ?

so d/2 = 16,000 / 10

= d/2 = log(1/10) (16,000) (maybe)

why? I'm confused, can anybody explain it(please) ?(2 votes)- log(16000) is a number that should be a little over 4 (think that log(10000) = 4). So I have no clue how you changed log(16000)=16000/10. So the opposite of dividing by 2 is multiply by which ends up with d=8.4 approximately.(3 votes)

- I have a question like

A bacterial culture grows according to the formula

p= p(subzero) of a to the power of t.

If it takes 5 days for the culture to triple in size, how long will it take to double in size?

I need help. What would a represent in this equation? Also how to tackle this problem? Thanks!(3 votes) - What do you do if the e is the t?(3 votes)

## Video transcript

- The bacteria in a Petri dish culture are self-duplicating at a rapid pace. The relationship between
the elapsed time T, in minutes, and the number
of bacteria, B of T, in the Petri dish is modeled
by the following function. And we see it's an exponential model here. How many bacteria will make up the culture after 120 minutes? So, really they just want to say, well what is B of 120 going to be? And so it's going to be 10 times two to the 120 divided by 12th power. So, this is going to be
equal to 10 times two to the, 120 divided by 12 is, 10th power. So this is going to be equal to 10 times, two to the 10th power is 1,024. If you want to verify that, you can say, well two to
the 5th is equal to 32, and so two to the 10th is going to be two to the 5th times two to the 5th. And 32 times 32 is... Let's see, 64. Zero. So, Let's see we're gonna have... Sorry, three times 32 is 96. Let's see you have a four and 12, 1024. So this is gonna be 1024. 10 times that is going to be equal to one zero two four zero. So, 10,200... 10,240 bacteria, and we're done.