Q2 Question 2 - Combining Functions 1On most state highways, the fine for speeding depends on the speed of the car. On a certain state highway, the fine for driving 70 mph is $25 and the fine for driving 85 mph is $100. On this particular road, when a car brakes suddenly, the function S(d) = √ (under the square root) 40d can be used to approximate the speed of a car (in mph) when it leaves a skid mark of length d feet on the road.
a) Using the information provided, write a linear equation that represents the fine for speeding, F,
as a function of the speed in mph on the state highway.
Part b) Find (F x S)(d) and explain what this function can be used for in context of the problem.

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Do some research and find a city that has experienced population growth. determine its population on january 1st of a certain year. write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. describe the variables and numbers that you used in your equation.

Tabby sells clothing at a retail store, and she earns a commission of 6.25% on all items she sells. last week she sold a pair of jeans for $32.50, a skirt for $18.95, and 2 blouses for $14.95 each. what was tabby's total commission? a $4.15 b $5.08 c $81.35 d $348.60