What is the value of the function at x = 2?

Answers

Answer 1

Answer:

check the picture below.

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A bacterial culture starts with 500 bacteria and doubles in size every half-hour.(a) How many bacteria are there after 3 hours?
Answer: 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?
Answer: 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?
Answer: 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.

Answers

Answer:

a). 32000

b). $T_(t)=500* 4^(t)$

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

$T_(n)=ar^(n)$

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

$T_(3)=500* 4^(3)$

$T_(3)=32000$

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

$T_(t)=500* 4^(t)$

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

That means duration 't' = 40 minutes of $(2)/(3)$ hours

By the formula,

$T_{(2)/(3)}=500* 4^{(2)/(3)}$

$T_{(2)/(3)}=1259.92$ ≈ 1259

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

After 3 hours, there will be 32,000 bacteria in the culture, given that the bacteria double in size every half-hour. The number of bacteria at any given time depends on whether they double precisely every half-hour or continuously within that timeframe.

In this scenario, the population growth of the bacterial culture follows exponential growth, where it doubles every half-hour. To calculate the number of bacteria after 3 hours (equivalent to 6 half-hours), you can use the formula for exponential growth: P(t) = P₀ * $2^{(t/h)$ , where P(t) is the population at time t, P₀ is the initial population, t is the time in hours, and h is the time interval for doubling (in this case, 0.5 hours). Plugging in the values, you get P(3) = 500 * $2^{(3/0.5)$ = 32,000 bacteria.

This means that after 3 hours, there will be 32,000 bacteria in the culture. The explanation also addresses the alternate interpretation of continuous growth, where the population increases continuously within each half-hour, resulting in approximately 1259 bacteria after 40 minutes.

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If h = 12 units and r = 4 units, what is the volume of the cone shown above? Use 3.14 for .

Answers

Answer:

≈ 201

Step-by-step explanation:

V= πr²h/3

V= 3.14*4²*12/3= 200.96 ≈ 201

The volume of the cone is 201.06 units³.

The volume of a cone is given by the formula:

Volume = (1/3) * π * r² * h

where r is the radius of the base and h is the height of the cone.

In this case, r = 4 units and h = 12 units. Using 3.14 for π, we can calculate the volume of the cone as follows:

Volume = (1/3) * 3.14 * 4² * 12

Volume = 201.06 units³

Therefore, the volume of the cone is 201.06 units³.

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A travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays. Which of the following types of bias affects the conclusions of the survey?a) Deliberate bias
b) Response bias
c) Non-response bias
d) Selection bias

Answers

Answer: Selection bias

Step-by-step explanation:

From the question, we are informed that a travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays.

The bus depicted above is referred to as the selection bias. The selection bias is simply a bias that is introduced when the sample obtained is not a representation of the population that the researcher wants to analyze. Here, the study population doesn't represent the target population.

The list gotten was for the people who made purchases using their credit cards but the agency used the list to determine the preference for air travel or train travel for taking holidays. This shows selection bias.

5. Expla in why 4 is or is not a multiplicative inverse mod 10 of 7.

Answers

Answer:

4 is not. (3 is)

Step-by-step explanation:

A number is the multiplicative inverse of 7 (mod 10) if the product mod 10 is 1.

7 × 4 mod 10 = 28 mod 10 = 8 . . . . not 1

) At a certain college, students are allowed to choose between online and in-person learning. 70% of the students choose online learning and 30% choose to come to campus for in-person instruction. Assume that the probability that a person studying online will contract the coronavirus is .02 and the probability that a person attending class in-person contracts the virus is .35 . (a) What is the probability that a person attending this college (either online or in-person) will contract the virus

Answers

Answer:

Probability = 0.119

Step-by-step explanation:

P (Coronavirus) = P(Person online & corona) or P(Person offline & corona)

(0.70 x 0.02) + (0.30 x 0.35)

0.014 + 0.105

0.119

What is the mean height, rounded to the nearest wholenumber if necessary?
The table shows the heights, in inches, of players on a girls'
basketball team.
Basketball Team Heights
70 68 72 66 68
69 66 71 74 66
66
068
69
70
Mark this and retum
Save and Exit
Next
SRL

Answers

Answer:

The mean height is 69 inches

Step-by-step explanation:

Add all of the values and divide by the number of terms

Mean is the averagevalue of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

The meanheight of the Basketballteam is 69.

What is a mean?

It is the averagevalue of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Basketball Team Heights

70 68 72 66 68

69 66 71 74 66

Sum of all the heights.

= 70 + 68 + 72 + 66 + 68 + 69 + 66 + 71 + 74 + 66

= 690

Number of heights = 10

Now,

The mean of the heights.

= 690/10

= 69

Thus,

The meanheight of the Basketballteam is 69.

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