1. Analyze and Interpret a Rational Function

The effluent from a gold mine is being filtered to reduce the particulate concentration of a toxic heavy

metal to a safe level. The function, C(x), represents the pollutant concentration in ppm as a function of

the number of filters that the effluent must pass through, x.

C(x)= ((2x)/(x+3))-((x-5)/(x+2))

a) Simplify the right side to a single fraction and then graph this function using DESMOS, clearly

showing the part of the graph that is in the practical domain.

b) State the equations of the Vertical Asymptotes and state the mathematical domain of this

function in interval notation.

c) Is this function a Case 1 or 2 Rational Function? State the equation of the Horizontal

Asymptote.

d) Which asymptote is relevant in the problem context? State the practical domain and range in

interval notation.

2. Interpreting a Basic Growth/Decay Exponential Function

The basic growth/decay exponential model is A(t)=Aob^(t/T)

The predicted future value of a commercial property in $ millions is a function of time, t , in years from 2020 is given by

A(t)=5(1.14^(t/3))

Interpret this function. Is this a growth or decay model? What is the current value of this property?

By what percentage is the value of this function increasing or decreasing on what time interval?

3. Graph and Analyze an Exponential Function

Progress is being made on the incidence of measles in an African country, as a result of an accessible

vaccination program. The number of diagnosed cases in thousands as a function of time, t , in years

from 2016 is given by

N(t)=16(2^(1-t))-1

a) Inspect the function and explain why this equation represents a decreasing function.

b) State the equation of the horizontal asymptote.

c) Find the intercepts and graph the function. Can the One-to-One Property of Exponentiation be

used to find the t-intercept?

d) State the practical domain and range of this function in interval notation.