Question

If the number of bacteria in a colony doubles every 210 hours and there is currently a population of 200 bacteria, what will the population be 420 hours from now?

Answer 1

Answer:

Since number of bacteria in a colony doubles every 210 minutes.

Therefore the function will be modeled by an exponential function with a common ratio of 2.

Currently the population is 8000 bacteria.

Therefore the expression will be

T_{n}=ar^{nk}T

n

=ar

nk

Here a = initial population

n = time or period

Tn = population after n minutes

k = constant

T_{210}=8000(2)^{210(k)}=16000T

210

=8000(2)

210(k)

=16000

2^{210k}=2^{1}2

210k

=2

1

210k = 1 ⇒ k=\frac{1}{210}k=

210

1

Now we have to find the population after 630 minutes.

T_{n}=ar^{nk}T

n

=ar

nk

T_{630}=8000(2)^{\frac{630}{210}}=8000(2)^{3}=64000T

630

=8000(2)

210

630

=8000(2)

3

=64000

Therefore the answer is option D). 64000 ; exponential function.