Hello please help me with these questions? Someone has answered these but without explanations and I want to know how you got the answer please. here are the supporting documents.

https://drive.google.com/drive/folders/1XWxpBdKnnVrD-xpL8diVF1LnvUdghuo_?usp=sharing

please help me to understand these questions.I have provided all the information through the share drive.

26. The profit function P(x) ...

27. The profit function P(x) ...

28. A researcher studies

29. For the year ..

30. The function ...

31. A local coffee shop found that its number of customers, N, could be predicted by the time of day in hours, t in the graph below t = 0 corresponds to the opening time of 5:00 a.m.

32. The graph below represents the projected year-end assets, A(t), in the Social Security trust fund in millions of dollars, where t represents the number of years since 2000 in the graph, t is defined between and including 0 to 50.

33. For the years ..

34. The function ...

35. A bank uses the funcion A(t) = 5000 (1.001)^12t calculate an acount balance, A, after t years.

What would be the account balance after 25 years?

A. A(25) =$5.000.00

B. A(25) = $6,748.28

C. A(5000.00) = $25

D. A(6748.28) =$25

36. Two companies have been trying to lower their travel costs since January of last year which corresponds to x = 0

37. The population of the United States, in millions of people, can be estimated with the function P(t) = 282(1.01)^t, where t= 0 represents the population, P, in the year 200 and t is measured in years.

What is the average rate al change of the popuation from t = 2 to t = 13?

A. The population increases at a rate of 2.560 milion people per year.

B. The population increases at a rate al 3.025 milion people per year.

C. The population increases at a rate of 287.668 mi on paople per year.

D. The population increases at a rate al 320.942 milion people per year.

38. A scientist found a sample of carbon-I4 and knows the function y = 116e^-000.12t models the exponential decay of carton-14 over t years.

How should the average rate of change over the time interval t = 35 to t = 85 be interpreted?

A. The amount of carbon-14 in the sample increases at a rate of 0.130 grams per year.

B. The amount of carbon-14 in the sample increases at a rate of 0.128 grams per year.

C. The amount of carbon-14 in the sample decreases at a rate of 0.130 grams per year.

D. The amount of carbon-14 in the sample decreases at a rate of 0.128 grans per year.

39. The value of a car

40. A logistic function was used to model the number of people who catch a certain virus, V, based on age (measured in t years). The function v(t) =

Assuming the model is accurate, do more 30-year-olds or 60-year-olds catch the virus?

A. More 60-year-olds catch the virus since V (30) < V (60).

B. More 30-year-olds catch the virus since V (30) < V (60).

C. More 60-year-olds catch the virus since V (30) > V (60).

D. More 30-year-olds catch the virus since V (30) > V (60).

41. A local gerbil population can be estimated with the function P(t) = , where t = 0 represents the gerbils population, p, in the year 2020 and t is measured in years.

What is P(5) rounded to the nearest integer, and what does it represent?

A. P(5) = 181, which means that in 2181, there are approximately 5,000 gerbils in the population.

B. P(5) = 204, which means that in 2040, there are approximately 5,000 gerbils in the population.

C. P(5) = 204, which means that in 2025, there are approximately 204 gerbils in the population.

D. P(5) = 181 which means that in 2025, thane are approximately 181 gerbils in the population.

42. The rate that a rumor spreads through a middle school can be determined using the function R(d) = , where R is the number of people who have heard the rumor after d days of it being introduced to the student body.

what is R(2) ?

A. R(2) = 61, so 61 people have heard the rumor after 2 days.

B. R(2) = 182, so 182 people have heard the rumor after 2 days.

C. R(2) = 61, so 2,000 people have heard the rumor after 61 days.

D. R(2) = 182, so 2,000 people have heard the rumor after 182 days.

43. A factory with an assembly line can produce more automobiles per week as more employees are working at a given time, limited by the capacity of the assembly line. The model follows the function below, where A is the number of automobiles per week, and w is the number of workers at a given time.

How is rate of change represented in context of this problem?

A. Automobiles per week

B. Automobiles per week per worker

C. Workers per week

D. Workers per automobile per week

44. The rate that a rumor spreads through a middle sohool can be modeled with a logistic function. The table below was produced using a logistic function, where Is the number of people who have heard the rumor after d days of it being introduced to the student body.

D R(d)

1 61

3 480

5 1520

7 1939

How should the average rate of change from day 1 to day 5 be interpreted?

A. The rumor is spreading at a decreasing rate of 365 people per day.

B. The rumor is spreading al a decreasing rate of 210 people per day.

C. The rumor is spreading at an increasing rate of 210 people per day.

D. The rumor is spreading at an increasing rate of 365 people per day.

45. A writer tracks and plots sales in the weeks folowing a book release as shown in the graph below.

46. A factory

47. A factory with an assembly line can produce more automobiles per week as more employees are morking at a given me, infected by the capacity line. The model follows the function below, where A is the number of automobiles produced per week, and w is the number of workers at a given time.

48. The number of people in an office building who have the flu can be modeled by be graph below, where F(1) represents the number of people with flu, F, on day 1 and d is measured in days.

49. The number of rats infected by a disease can be modeled by the graph below, where S(1) represents the number of rats infected, S, on day 1, and d is measured in days.

When will approximately 75% of the maximum number of rats be infected?

A. On day 4

B. On day 9

C. On day 6

D. On day 7

50. The followinggraph measures fromvending machinesat a large business on a typical day.