Question

A scientist started with a culture of 10 bacteria in a dish. The number of bacteria at the end of each successive minute increased exponentially, so that the number at the end of one hour was 500. How many hours (to the nearest hour) from the start of the experiment passed before there were 1,000,000 bacteria?

Answer 1

Answer: 3 hours

Step-by-step explanation: Exponential growth is a model showing a specific quantity increasing over time.

The formula for it is $y(t)=A_{0}e^{kt}$

in which

y(t) is the quantity after time t

A₀ is initial value

k is rate of growth

t is time

To determine how much time has passed, first find the rate of growth and knowing that 1 hour has 60 minutes:

$500=10e^{60k}$

$e^{60k}=50$

$60k=ln(50)$

k = 0.065

With the rate, determine the time

$10^{6}=10e^{0.065t}$

$e^{0.065}=10^{5}$

$0.065t=5ln(10)$

t = 177.12 minutes

The amount of hours passed is

$t=\frac{177.123}{60}$

t = 3

From the start of the experiment, it has passed 3 hours before there were 1,000,000 bacterias.