For any two linear functions fx ax b and gx cx d is f g

For any two linear functions f(x) = ax + b and g(x) = cx + d is f g the same g f? A population of 20 rabbits is introduced to a small island. The population increases at a rate 60% per year. Find a function f(t) that represents the number of rabbits on the island after t years. Suppose 100 rabbits were introduced to the island and g(t) is the number of rabbits after t years. Describe the stretching or shrinking operations that must be performs on the functions y = f(t) to obtain the function y = g(t). Write the new function y = g(t) that results from this transformation. Two 5-grain tablets contain 650 mg of the drug with aspirin\'s half-life of 29 minutes. How much is left in the bloodstream after 2 hours? How long does it take for the level to be equivalent to 10 mg of aspirin? If an individual takes two tablets every 4 hours, what is the maintenance level of the aspirin? The table shows the average number of tornados reported in the United States per month based on historical records. Determine a sinusoidal function that models the monthly number of tornados as a function of time. Determine the magnitude of the position vectors from the origin to the following points. (3, 4) (12, 5) (3, -2) (-7, -3)

Solution

1) f(x) = ax +b ; g(x) = cx +d

(f o g)(x) : plug x = g(x) in f(x)

(f o g)(x) =a(cx +d) +b = acx +ad +b

(g o f)(x) = c(ax +b) +d

= cax +bc +d

(f o g)(x) is not equal to (g o f)(x)

2)

a) intial pop. = 20 rabbits

every increases by 60% = 20(1.6)

After t years Population, f(t) = 20(1.6)^t

f(t) = 20(1.6)^t

b) So, if 100 rabits were introduced then g(t) = (20+100)(1.6)^t = 120(1.6)^t

= 6[20(1.6)^t]

So, f(t) is stretched by 6units to get g(t)