Question

If the number of bacteria in a colony doubles every 210 minutes and the population is currently 8,000 bacteria, what will the population be in 630 minutes and is it modeled by a linear function or a exponential function? A) 24,000; linear function B) 24,000; exponential function C) 64,000; linear function D) 64,000; exponential function

Answer 1

Answer:

Option D. 64000 ; exponential function.

Step-by-step explanation:

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

$T_{n}=ar^{nk}$

Here a = initial population

n = time or period

Tn = population after n minutes

k = constant

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

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

210k = 1 ⇒ $k=\frac{1}{210}$

Now we have to find the population after 630 minutes.

$T_{n}=ar^{nk}$

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

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

Answer 2

Answer:

36,00 bacteria

Step-by-step explanation:

First, find out how many times the population will double. Divide the number of hours by how long it takes for the population to double.

672÷336=2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

9,00022=36,000

That calculation could also be written with exponents:

9,00022=36,000

After 672 hours, the population will be 36,000 bacteria.