Question

The population of a certain species of bacteria doubles every hour. Use the following

exponential population equation to determine the amount of time it would take a population of
1 bacteria to grow to 1024. = 0(2)^t
(Please show steps:))

Answer 1

The bacteria will grow from 1 to 1024 in 10 hours

Explanation:

Given

P_0 = 1

P = 1024

We have to find time

Putting values in the formula

`P = P_0(2)^t\\1024=(1)(2)^t`

Anything multiplied with 1 remains the same

`1024=2^t\\2^(10) = 2^t`

Using the property "when bases are same, the exponents can be put equivalent"

t = 10 hours

Therefore, the bacteria will grow from 1 to 1024 in 10 hours ..