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

Lesson 15: Topic C: Lessons 20-21: Inverse relationship of exponentials and logarithms

# 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?
• 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.
• Wondering why this video is included in the Algebra II logarithms section. The problem doesn't require the use of logarithms.
• 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.
• Shouldn't you divide by 120 for the last step?
• 120 is the amount of time given, so you don't divide by 120.
• 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?
• 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.
• 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?
• 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.
• At where did 2^5 come from?
• 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.
• 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.
• We multiplied both sides by -25. -25·(-0.04)=1, so we just have t on the left-hand side.
• 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) ?
• 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.