# Suppose that the population of a colony of bacteria increases exponentially. If the population at the start is 300 and 4 hours later it is 1800, how long (from the start) will it take for the population to reach 3000?

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**A)** #"4 ln10"/"ln6"# #"hrs"#

**B)** #"6/(4ln10)# #"hrs"#

**C)** #"(10ln4)/ln6# #"hrs"#

**D)** #"4(ln10-ln6)# #"hrs"#

Answer is **A)**.

Thanks in advance!

**A)**

**B)**

**C)**

**D)**

Answer is **A)**.

Thanks in advance!

##### 1 Answer

#### Answer:

See below.

#### Explanation:

We need get an equation of the form:

Where:

We are given:

We need to find the growth/decay factor:

Divide by 300:

Taking natural logarithms of both sides:

Divide by 4:

Time for population to reach 3000:

Divide by 300:

Taking logarithms of both sides:

Multiply by 4:

Divide by