Correct answers only 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.]

B

Step-by-step explanation:

1.6 = t

Option B. 1.6 Hours

Step-by-step explanation:

The model for the population of bacteria is growing by :

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.

⇒

⇒

Taking the natural log in on both the side

⇒

⇒

⇒

⇒ t = 1.6 hours

Therefore, The correct option is B). 1.6 hours

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

8

step-by-step explanation: