1.The table shows the population, in millions, of the planet Romulus, which is increasing at a constant rate.
year / 2010 / 2020Population of Romulus (millions) / 16 / 20
- Define your independent and dependent variables.
- Write the equation, using function notation, for the growth of the planet Romulus. If necessary, round values to 3 decimals. Show your work.
2.Given that the equation for the population (P) of Romulus, in millions, as a function of the number of years (t) since 2010 is
- What is the slope of P(t)? Interpret this value in the context of the problem.
- During which year will the population of Romulus reach 25,000,000 people? Show your work.
3.The table shows the population, in millions, of the planet Vulcan, which is increasing by a constant percentage.
Year / 2010 / 2020Population of Vulcan (millions) / 8 / 12
Write the equation, using function notation, for the population (P) growth, in millions, of the planet Vulcan as a function of the number of years since 2010 (t). If necessary, round values to 3 decimals. Show your work.
4.Given that the equation for the population (P) of Vulcan, in millions, as a function of the number of years (t) since 2010 is
- What is the growth rate of P(t)? Interpret this value in the context of the problem.
- Algebraically determine during which year will the population of Vulcan reach 35,000,000 people? Show your work.
5.A CD warehouse charges you $45 for ordering 10 CDs and $81 for ordering 22 CDs, including a fixed shipping and handling fee.
a.Write the linear equation that models this situation, using function notation. Assume that the cost of the CDs is a function of the number of CDs ordered.
b.What is the slope of your equation? Interpret this value in the context of the problem.
- What is the vertical intercept of your equation? Interpret this value in the context of the problem.
6.The loudness (L) of a sound (measured in decibels, dB) is indirectly proportional to the square of the distance (d) from the source of the sound. A person 10 feet from a lawn mower experiences a sound level of 70 dB.
a.Write the exact formula that describes this situation after determining the constant of proportionality.
b.How far away is a person who experiences a sound level of 200 dB?
c.What is the loudness for a person 100 feet away?
7.Let be the parent function.
a.What is the vertical intercept of ?
b.Give the equation of any asympototes of .
c.Describe the transformations that were performed on to obtain:
- Give the equation of any asympototes of .
8.Let be the parent function.
Create a new function, , that is shifted right 1 unit, vertically compressed by a factor of 0.25 and shifted down 1.
9.Given the parent function f(x), draw the following transformations.
a.
b.
10.A baseball is hit so that its height (s), in feet, after t seconds is
- How high was the ball when it was hit?
- How high was the ball after 1 second?
- Find the maximum height of the ball.
11.A baseball is hit so that its height (s), in feet, after t seconds is
- When does the ball reach a height of 28 feet?
b.When does the ball hit the ground?
c.What is a reasonable domain for this function?
12.Create the function that models this situation. Define your independent and dependent variables.
20 tons of pollutant was dumped into a lake, and each year its amount in the lake is reduced by 25%.
13.Create the function that models this situation. Define your independent and dependent variables.
The heat experienced, in degrees Fahrenheit, by a hiker at a campfire is inversely proportional to the cube of his distance, in feet, from the fire with a constant of proportionality of 600.
14.Due to a hole in your pocket, the amount of quarters in your pocket,Q, is a function of the time you’ve been walking t, in minutes, is given by: .
a.Find the inverse of Q and use correct notation.
b.Findand and explain what each means in the context of the problem.
Match each of the folowing functions with its graph. Assume a, c > 0.
_____ ______ _____
_____ _____ ______
______ ______ ______
______ ______ ______
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