Question

A culture of 10 bacteria is started, and the number of bacteria will double every hour. In about how many hours will there be 3,000,000 bacteria?
Can some show me how to do this step by step using logarithm?

I will mark BRAINLIEST for whoever gives the best and correct answer

thank you

Answer 1

Answer: it will take 18.2 years

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

a represents the initial amount of bacteria.

t represents the doubling.

From the information given

a = 10

t = 1 hour

Since after 1 hour, the amount of bacteria multiplies by 2, then

y = 2 × 10 = 20

Therefore

20 = 10 × b^1

Dividing through by 10, it becomes

2 = b

The equation becomes

y = 10(2)^t

For 3,000,000 bacteria, then

3000000 = 10(2)^t

3000000/10 = (2)^t

300000 = (2)^t

Taking log of both sides, it becomes

Log 300000 = tlog2

5.477 = 0.301t

t = 5.477/0.301

t = 18.2 years