MAT 117 Arizona State University Math Variable Terms Questions

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MAT 117

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

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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 Jennie’s skin cells were burned when she escaped from a fire. If 3.7 × 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 𝑅 = equation for T, which is the temperature in degrees Kelvin. 𝑃𝑉 𝑛𝑇 . 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 Yifei’s age when they were married. (The variable should represent Yifei’s 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 𝐶 = 37000 100−𝑝 , 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 𝑥 is the number of years since 2009 and 𝑓(𝑥) is the number of vehicles sold, find the equation of the line through these two points. c. [2 pts] Assuming 𝑓(𝑥) 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] 252𝑥+3 = 3125 b. [3 pts] 42𝑥−1 = 8𝑥+3 2. The population growth in Gilbert AZ can be modeled by the function P (t )  6545.52e 0.149t where 𝑃 is the population and 𝑡 is the number of years since 1980. a. [2 pts] What is the growth rate for 𝑃(𝑡)? 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 𝑃(𝑡) = 50(1+0.05𝑡) 2+0.01𝑡 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  x  700 and 0  y  300 . Be sure to indicate the scale on the graph, at least 2 points and any asymptotes.
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Explanation & Answer

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1. Scientific Notation and Percent. (Based on the ideas in Objective 1 and Objective 4.) (6
points)
Two percent of Jennie’s skin cells were burned when she escaped from a fire. If 3.7 × 1010 of
her skin cells were burned then, how many skin cells were not burned?
Sol: Let x be the total number of skin cells.
As given that 2% of total skin cells are burnt skin cells which are, 3.7 × 1010 . So,
2% 𝑜𝑓 𝑥 = 3.7 × 1010
2
(𝑥) = 3.7 × 1010
100
2𝑥 = 3.7 × 1010 × 100
2𝑥 = 3.7 × 1010+2
2𝑥 = 3.7 × 1012
3.7 × 1012
𝑥=
2
𝑥=

3.7
× 1012
2

𝑥 = 1.85 × 1012
The total number of skin cells is 1.85 × 1012 . Now the number of skin cells that are not burnt
is
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 𝑇𝑜𝑡𝑎𝑙 − 𝐵𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 1.85 × 1012 − 3.7 × 1010
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 1.813 × 1012
Hence.
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 + 𝑃𝑟𝑡. Solve this equation for P, which is the amount of principal (initial
investment) needed.
Sol: Given
𝐴 = 𝑃 + 𝑃𝑟𝑡

Taking P common, we get
𝐴 = 𝑃(1 + 𝑟𝑡)
Now dividing both sides by (1 + 𝑟𝑡), we get
𝐴
𝑃(1 + 𝑟𝑡)
=
(1 + 𝑟𝑡)
(1 + 𝑟𝑡)
𝐴
=𝑃
(1 + 𝑟𝑡)
𝑃=

𝐴
(1 + 𝑟𝑡)

Or
𝑃 = 𝐴(1 + 𝑟𝑡)−1
Hence.
B. [4 pts] The pressure, temperature, and volume of an ideal gas are related by the equation

𝑅=

𝑃𝑉
𝑛𝑇

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

Sol: Given
𝑅=

𝑃𝑉
𝑛𝑇

Multiplying both sides by T, we get
𝑅×𝑇 =

𝑃𝑉
×𝑇
𝑛𝑇

𝑅𝑇 =

𝑃𝑉
𝑛

Now dividing by R on both sides, we get
𝑃𝑉
𝑅𝑇
= 𝑛
𝑅
𝑅
𝑇=
Hence.

𝑃𝑉
𝑛𝑅

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...


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