The admissions office at a public university estimates that 65% of the students offered admission to the class of 2019 will actually enroll. a. Find the linear function y = N ( x), where N is the number of students that actually enroll and x is the number of all students offered admission to the class of 2019. b. If the university wants the 2019 freshman class size to be 1350, determine how many students should be admitted.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
112. [T] The admissions office at a public university estimates that 65% of the students offered
admission to the class of 2019 will actually enroll.
a. Find the linear function y = N ( x), where N is the number of students that actually enroll and x is
the number of all students offered admission to the class of 2019.
b. If the university wants the 2019 freshman class size to be 1350, determine how many students
should be admitted.
103. [T] A company purchases some computer equipment for $20,500. At the end of a 3-year period,
the value of the equipment has decreased linearly to $12,300.
a. Find a function y = V(t) that determines the value V of the equipment at the end of t years.
b. Find and interpret the meaning of the x - and y -intercepts for this situation.
c. What is the value of the equipment at the end of 5 years? d. When will the value of the equipment
be $3000?
104. [T] Total online shopping during the Christmas holidays has increased dramatically during the
past 5 years. In 2012 (t = 0), total online holiday sales were $42.3 billion, whereas in 2013 they were
$48.1 billion.
a. Find a linear function S that estimates the total online holiday sales in the year t.
b. Interpret the slope of the graph of S.
c. Use part a. to predict the year when online shopping during Christmas will reach $60 billion.
105. [T] A family bakery makes cupcakes and sells them at local outdoor festivals. For a music
festival, there is a fixed cost of $125 to set up a cupcake stand. The owner estimates that it costs
$0.75 to make each cupcake. The owner is interested in determining the total cost C as a function
of number of cupcakes made.
a. Find a linear function that relates cost C to x, the number of cupcakes made.
b. Find the cost to bake 160 cupcakes.
c. If the owner sells the cupcakes for $1.50 apiece, how many cupcakes does she need to sell to start
making profit? (Hint: Use the INTERSECTION function on a calculator to find this number.)
106. [T] A house purchased for $250,000 is expected to be worth twice its purchase price in 18 years.
a. Find a linear function that models the price P of the house versus the number of years t since the
original purchase.
b. Interpret the slope of the graph of P.
c. Find the price of the house 15 years from when it was originally purchased.
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