Question

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!

A population of bacteria is growing according to the exponential model P = 100e^(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]

Answer 1

Answer: B

Step-by-step explanation:

$P=100e^{(.70)t}$

$300=100e^{.7t}$

$3=e^{.7t}$

$ln3=lne^{.7t}$

$ln3=.7t$

$\dfrac{ln3}{.7}=t$

1.6 = t

Answer 2

Answer:

Option B. 1.6 Hours

Step-by-step explanation:

The model for the population of bacteria is growing by :

$P=100e^{(0.70)t}$

Where P = Number of colonies

and t = time in hours.

So, now put  the value of  P = 300 in the given model and obtain the value of t.

⇒ $300=100e^{(0.70)t}$

⇒ $3=e^{(0.7)t}$

Taking the natural log in on both the side

⇒ $In3=Ine^{(0.7)t}$

⇒ $In3=0.7t$

⇒ $t=\frac{In3}{0.7}$

⇒ t = 1.6 hours

Therefore, The correct option is B). 1.6 hours