The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 2.5% per hour. How many hours does it take for the size of the sample to double?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

Question

The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 2.5%  per hour. How many hours does it take for the size of the sample to double?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

hero · Answer

The doubling time is the period of time it takes for a given quantity to grow by 100%

Exponential Growth Formula (for doubling time):
$$2A_0 = A_0b^t$$Where
$A_0$ = initial quantity
2A = twice the size of the initial quantity
b = growth rate (1 + r%)
t = the period of time it takes to get from A to 2A

In this case, 
$b = 1 + .25$

$2A_0 = A_0(1 + .25)^t$

After simplification:
$2 = (1.25)^t$

@ilikesunflowers, Can you finish solving for t here?

anonymous · Answer

27.73 hours?

hero · Answer

How exactly did you get that? Show me your steps please.

anonymous · Answer

t = ln(2)/.025 = 27.73 hours

hero · Answer

You have to take log of BOTH sides first before isolating t

hero · Answer

$$\log(2) = \log(1.25)^t$$