Question

In a lab, a colony of 100 bacteria is placed on a petri dish. The population triples every hour.

1. How would you estimate or find the population of bacteria in:

a. 4 hours?

b. 90 minutes?

c. 72 hour?

Answer 1

a). 8100 bacteria

b). 519 bacteria

c). Infinite

Explanation:

Population growth of a bacteria is given by the exponential function,

f(x) =
`P_(0)(1+(r)/(100))^(t)`

Where f(x) = Population after time 't'

`P_(0)` = Initial population

r = Growth rate

t = Duration after t hours

If "100 bacteria gets tripled every hour"

300 =
`100(1+(r)/(100))^(1)`

3 = 1 +
`(r)/(100)`

r = 100×(3 - 1)

r = 200

So the function is, f(x) =
`100(3)^(t)`

a). Population after 4 hours,

f(4) =
`100(3)^(4)`

= 8100 bacteria

b). Population after 90 minutes Or 1.5 hours

f(1.5) =
`100(3)^(1.5)`

= 519.61

≈ 519 bacteria

c). Population after 72 hours,

f(72) =
`100(3)^(72)`

= Infinite