Question 4
Answer: Choice D) 0 <= x <= 30, -3
The domain is the set of allowed x inputs of a function. The smallest x can be in this case is x = 0. The largest is x = 30. So 0 <= x <= 30 is our domain here.
Calculate the slope of the line through (0,90) and (30,0) to find the average rate of change over the entire domain
m = (y2-y1)/(x2-x1)
m = (0-90)/(30-0)
m = -90/30
m = -3
The average rate of change over the entire domain is -3. This means the population is decreasing by 3 bacteria per minute on average if we consider the entire domain (basically the entire lifetime of the bacteria sample).
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Question 13
Answer: Choice C) original populations are equal for both states
To show why this answer works, plug x = 0 into the f(x) function
f(x) = 2*(1.08)^x
f(0) = 2*(1.08)^0
f(0) = 2
The initial population of state A is 2 million people.
State B also starts with 2 million people because of the y intercept (0,2), which is where the graph crosses through the vertical y axis number line.
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Question 15
Answer: Choice A) exponential increases faster
The exponential may start off slowly, but over time the exponential growth rate ramps up and the growth rate gets faster and faster (ie accelerates more). The linear function will grow at the same rate no matter what.