Abacterial culture starts with 500 bacteria and doubles in size every half-hour.
(a) how many bacteria are there after 3 hours?
since 3 hours equals 6 half-hours, the culture will have doubled 6 times.
therefore, there will be
500 · 2
6 = 32,000
bacteria.
(b) how many bacteria are there after t hours?
since t hours is the same as 2t half-hours, the culture will have doubled 2t
times. therefore, there will be
500 · 2
2t
bacteria.
(c) how many bacteria are there after 40 minutes?
there are two possible answers depending on how you interpret the set-up
to the problem. if each bacterium in the culture doubles once every half-hour on the
half-hour, then each one will double after exactly 30 minutes, and then not again until
60 minutes have passed. in that case, there will be
500 · 2 = 1000
4
bacteria after 40 minutes.
on the other hand, if each bacterium doubles exactly once per half-hour, but at some
random time within that half-hour, then it makes sense to think of the population
function p(t) = 500 · 2
2t as continuous. in that case, since 40 minutes is
40
60
=
2
3
of an hour, the population will be
500 · 2
2
2
3 = 500 · 2
4
3 ≈ 1259
after 40 minutes.

a). 32000

b).

c). 1259

Step-by-step explanation:

Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.

Sum of the bacterial population after t hours will be represented by

Where a = population at the start

r = ratio with the population is growing

n = time or duration of the growth in one hour

a). Population of 500 bacteria gets doubled after half an hour.

Or gets 4 times after an hour

This sequence will have a common ratio r = 4

and initial population a = 500

Therefore, population of the bacteria after 3 hours will be

b). After t hours number of bacteria will be represented by

c). We have to calculate the population after 40 minutes.

That means duration 't' = 40 minutes of hours

By the formula,

≈ 1259

Therefore, number of bacteria after 40 minutes will be 1259.

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

A represents the initial amount of bacteria.

t represents the doubling time.

From the information given

A = 500

t = 1/2 hours

Since after 1/2 hours, the population doubles, then

y = 2 × 500 = 1000

Therefore

1000 = 500 × b^1/2

2 = b^1/2

Raising both sides of the equation by 2, it becomes

2^2 = b^1/2 × 2

b = 4

The equation becomes

y = 500 × 4^t

Therefore, the population in 3 years time would be

y = 500 × 4^3

y = 32000

b) The number of bacteria after t years is

y = 500 × 4^t

c) To determine the number of bacteria after 40 minutes, we would first convert 40 minutes to hours. It becomes

40/60 = 2/3 hours. Therefore

y = 500 × 4^2/3

y = 1259

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )