Question

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

Answer 1

Answer:

a). 8100 bacteria

b). 519 bacteria

c). Infinite

Step-by-step explanation:

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

f(x) = $P_{0}(1+\frac{r}{100})^{t}$

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 = $100(1+\frac{r}{100})^{1}$

3 = 1 + $\frac{r}{100}$

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