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45 votes
45 votes
Math help please

Thanks
A lot

Math help please Thanks A lot-example-1
User Jfortunato
by
3.0k points

1 Answer

21 votes
21 votes

Answer:

2 hours: 3968 [I don't understand the $ sign in the answer box]

At midnight: 12137

Explanation:

The bacteria are increasing by 15% every hour. So for every hour we will have what we started with, plus 15% more.

The "15% more" can be represented mathematically with (1 + 0.15) or 1.15. Let's call this the "growth factor" and assign it the variable b. b is (1 + percent increase).

Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450

At the end of the second hour we're increased by 15% again:

(3450)*(1.15) = 3968.

Each additional hour add another (1.15) factor, If we assign a to be the starting population, this can be represented by:

P = a(1.15)^t for this sample that increase 15% per hour. t is time, in hours.

If a represents the growth factor, and P is the total population, the general expression is

P = ab^t

Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM. That is a 10 hour period, so t = 10

P = (3000)*(1.15)^10

P = 12137

User Tigrou
by
3.1k points
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