Please HELP with this question?

Question

A population of bacteria doubles every hour. How many minutes will it take for the population to reach 25,500 if there are 75 at the start?

a) 8.4
b) 20.9
c) 1252
d) 505

Answer 1

25500 / 75
= 340

log (base 2) 340
=8.4093909361377...

60 * 8.4093909361377...
=504.563456168262

The closest answer is d).

Answer 2

The number of bacteria at any given hour can be modeling using the function f(x)=75*(2^x), where x is the number of hours. We want the number of bacteria to be 25,500, so we want 25,500 = 75(2^x) and now solve for x. Take a logarithm of both sides and use the laws of logs:

1) ln(xy)=ln(x)+ln(y)
2) ln(x/y)=ln(x)-ln(y)
3) ln(x^r)=rln(x)

We have ln (25,500) = ln(75*(2^x))

ln(25,500)=ln(75)+xln(2)
ln(25,500)-ln(75)=xln(2)
ln(25,500/75)/ln(2)=x.

Here x is 8.4. Now this is the number of hours. To get minutes, multiply by 60. So we have 505 minutes.

Answer 3

Since they double every hour, the first hour there would be 2 times the original amount, the second hour there would be 4 the original amount, the third hour, 8 times the original amount, etc. This is equivalent to 2^n, where n is the number of hours.

Therefore:

75 * 2^n = 25,500

2^n = 340

n * ln2 = ln340

n = 8.41

Now we convert n from hours to minutes:

8.41 * 60 = 504.56

Answer d.

Answer 4

let h the hour so 75*2^h = 25500 -> 2^h = 25500/75 -> h = log(340) in 2
60 * h is the answer

Answer 5

It's about 8 1/2 hours. Closest answer is d. 510 is what I got.

Hope that helps.

Answer 6

this question is based on geometric progression
here a=75 r=2
to find n

25500=75(2^n-1)
2^n-1=340
2^n=341
n=log341 * 60 min
2
n=504.877076411 min

Answer 7

75 x 2 ^ n = 25500

n represents the number of hours.

solve for n, then convert that to minutes.

i get d.