Mathematics, 06.05.2020 08:06 bryanmcmillianjr

The doubling time of a bacterial population is 15 minutes. After 80 minutes, the bacterial population was 60000.

-What was the initial population of bacteria?

-Using your rounded answer from above, find the size of the bacterial population after 3 hours.

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Answer from: shavonfriend27

The initial population of bacteria was 1488.

The size of the bacterial population after 3 hours will be 6,084,093

Step-by-step explanation:

The population of bacteria after t minutes can be modeled by the following equation.

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate.

The doubling time of a bacterial population is 15 minutes.

This means that P(15) = 2P(0) . We use this to find r.

$P(t) = P(0)e^{rt}$

$2P(0) = P(0)e^{15r}$

$e^{15r} = 2$

$\ln{e^{15r}} = \ln{2}$

$15r = \ln{2}$

$r = \frac{\ln{2}}{15}$

r = 0.0462

After 80 minutes, the bacterial population was 60000.

This means that P(80) = 60000 . So

$P(t) = P(0)e^{0.0462t}$

$60000 = P(0)e^{0.0462*80}$

$P(0) = \frac{60000}{e^{0.0462*80}}$

P(0) = 1488

This means that the initial population of bacteria was 1488.

Using your rounded answer from above, find the size of the bacterial population after 3 hours.

t is in minutes, so this is P(3*60) = P(180).

$P(t) = 1488e^{0.0462t}$

$P(180) = 1488e^{0.0462*180}$

P(180) = 6,084,093

The size of the bacterial population after 3 hours will be 6,084,093

Answer from: Quest

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 ☺

Answer from: Quest

step-by-step explanation:

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