What is the greatest number of bottles Corrine can put sand in?
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Question:
A population of insects, in thousands, can be modeled using the function
, where t is time in months. Which statement best
describes the population of insects?
A. The population is decaying at a rate of 3% each month.
B. The population is decaying at a rate of 25% each month.
C. The population is growing at a rate of 75% each month.
D. The population is growing at a rate of 97% each month.
Answer:
A. The population is decaying at a rate of 3% each month.
Step-by-step explanation:
Given
Required
True statement about the function
From the options, we can see that we are to answer the question on the basis of decay and growing rates.
An exponential form is:
Compare to
If , then
r represents growth rate
else, r represents decay rate
Since b < 0.97:
The slope m of a line
through points 
and 
is given by :<span>
Thus, the slope of the line passing through points </span><span>(−1, 7) and (2, 10) is
</span>
<span>
The equation of a line with slope m passing through a point P(a, b) is given by
(y-b)=m(x-a).
We can consider any of the points (-1, 7), or (2, 10). Let's choose (2, 10):
y-10=1(x-2)
y-10=x-2
y-x=-2+10
y-x=8
Answer: </span><span>C. −x+y=8</span>
Thus, the slope of the line passing through points </span><span>(−1, 7) and (2, 10) is
</span>
<span>
The equation of a line with slope m passing through a point P(a, b) is given by
(y-b)=m(x-a).
We can consider any of the points (-1, 7), or (2, 10). Let's choose (2, 10):
y-10=1(x-2)
y-10=x-2
y-x=-2+10
y-x=8
Answer: </span><span>C. −x+y=8</span>