simple mat 177 queastions, plz show every step of each queastions clearly, thanks

MAT 117- Problem Set 1

Objectives 1-4

Directions: Complete the problems on the answer sheet provided. All problems must be completed by the end of

class to earn full credit. Show all work.

1. Scientific Notation and Percent. (Based on the ideas in Objective 1 and Objective 4.) (6 points)

Two percent of Jennieβs skin cells were burned when she escaped from a fire. If 3.7 Γ 1010 of her skin cells

were burned then, how many skin cells were not burned?

2. Solving for a variable in terms of other variables. (From Objective 4.)

A. [4 pts] The equation for the future value of a simple interest investment is given by the equation A = P + P r t.

Solve this equation for P, which is the amount of principal (initial investment) needed.

B. [4 pts] The pressure, temperature, and volume of an ideal gas are related by the equation π
=

equation for T, which is the temperature in degrees Kelvin.

ππ

ππ

. Solve this

3. (Based on ideas in Objective 2.) 6 points

Xavier and Yifei have been married for exactly 37 years. Yifei is four years older than Xavier. Now the sum of

their ages is 124. How old was Yifei when they were married?

a. Set up and write an equation that represents the unknown ages in terms of Yifeiβs age when they were married.

(The variable should represent Yifeiβs age when they were married.)

b. Determine how old Yifei was when Yifei and Xavier were married.

4. (Based on ideas in Objective 3.) 5 points

The cost of cleaning up pollution in a stream is given by πΆ =

37000

100βπ

, where C is the cost in dollars to clean p

percent of the stream. (For instance, when p is 20, then the formula will calculate the cost to clean up 20 percent

of the stream.) p must be greater than or equal to zero and p must be less than what number? Why?

MAT 117- Problem Set 2

Objective 5-9

Directions: Complete the problems on the answer sheet provided. All problems must be completed by the end of class

to earn full credit. Show all work.

1. In 2009 the number of vehicle sales in the United States was 10,602 thousand and in 2013 it was 15,884 thousand.

a. [3 pts] Determine the average rate of change (slope) from 2009 to 2013.

b. [3 pts] If π₯ is the number of years since 2009 and π(π₯) is the number of vehicles sold, find the equation of the

line through these two points.

c. [2 pts] Assuming π(π₯) is a linear function, use the equation to predict the number of vehicles sold in 2016.

2. [8 pts] A scientist mixes water (containing no salt) with a solution that contains 40% salt. She wants to obtain 176

ounces of a mixture that has 5% salt. How many ounces of water (containing no salt) and how many ounces of the

40% salt solution should she use?

3. [9 pts] Last year, Singh had $20,000 to invest. He invested some of it in an account that paid 7% simple interest per

year, and he invested the rest in an account that paid 6% simple interest per year. After one year, he received a total

of $1280 in interest. How much did he invest in each account?

MAT 117- Problem Set 4

Objectives 16-18

Directions: Complete the problems on the answer sheet provided. All problems must be completed by the end of class

to earn full credit. Show all work.

1. Solve the exponential equations. Report your answers as fractions or integers

a. [3 pts] 252π₯+3 = 3125

b. [3 pts] 42π₯β1 = 8π₯+3

2. The population growth in Gilbert AZ can be modeled by the function P (t ) ο½ 6545.52e 0.149t where π is the

population and π‘ is the number of years since 1980.

a. [2 pts] What is the growth rate for π(π‘)?

b. [1 pt] What was the population in 1980?

c. [4 pts] Find P (11) and explain what it means in the context of the problem.

d. [3 pts] What is the projected population of Gilbert in 2019?

3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists

declared the insect endangered and transplanted the insect to a protected area. The population P (in thousands )of

the insect in t months after being transplanted is π(π‘) =

50(1+0.05π‘)

2+0.01π‘

a. [3 pts] Determine the number of months until the insect population reaches 40 thousand.

b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your answer.

c. [3 pts] Sketch a graph of the function using the window 0 ο£ x ο£ 700 and 0 ο£ y ο£ 300 . Be sure to indicate

the scale on the graph, at least 2 points and any asymptotes.