Problem Solving

A biologist finds that she can perfectly model the population growth G of a bacteria colony after n days using the function g=5,000((1+b/50)^n -1), where b represents the colony's birth rate in cells per day. If the biologist takes this birth rate to be a fixed value, is the rate greater than 100 cells per day?

1. The population growth after 4 days is 1,275,000 cells
2. (1+b/50)^4 > 75




OA: A


Thoughts on how to attack this problem would be appreciated. Took me way too long to solve

"is the rate greater than cells per day?"

is there supposed to be a number in there somewhere?

Yes--greater than 100. Sorry about that.

Okay. Thanks.

With statement 1 you're given a value of G and a value of n, so the equation would become 1,275,000=5,000(1+b/50)^3. You can solve this for a unique value of b (though you shouldn't bother actually doing it) and then you could see if it's bigger than 100. Don't do it. Just realize that you COULD do it and it would give you a definite yes or no.

With statement 2, you could solve the inequality for b as follows, assuming b is non-negative because it is a birth-rate:

1+b/50>75^(1/4)
b/50>75^(1/4)-1
b>50*75^(1/4)-50.

75 is close to 81 and 81^(1/4)=3. so 75^(1/4)is a little less than 3. 50*(a little less than 3) is a little less than 150. Subtract 50, and the expression is slightly less than 100.

So b> (slightly less than 100).

So there is a little bit of room for the value of b to be less than 100. Or it could be greater than 100. Therefore, statement 2 is insufficient.

Ans: A

Thanks. That was actually much easier than I thought!

briology wrote:A biologist finds that she can perfectly model the population growth G of a bacteria colony after n days using the function g=5,000((1+b/50)^n -1), where b represents the colony's birth rate in cells per day. If the biologist takes this birth rate to be a fixed value, is the rate greater than 100 cells per day?

1. The population growth after 4 days is 1,275,000 cells
2. (1+b/50)^4 > 75




OA: A


Thoughts on how to attack this problem would be appreciated. Took me way too long to solve

Kindly check out the below link for video solution:

https://www.youtube.com/watch?v=jxOKEpOJrOA

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