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3 years ago

A slope of -4 and a y-intercept of 12. *

Mathematics

1 answer:

Luda [366]3 years ago

5 0

Answer:

I'm not sure what your question is but let me give you a little math lesson. when you have a y intercept, the number given is your y coordinate, that is at what point on the y axis your line is crossing. so on this line we have the point (0,12) we know this because the line crosses on the y axis so therefore our x value has to be zero.

Because they have given us the slope you simply start at an already known coordinate. (0,12) and use the old rise over run rule. because the slope is negative you know your line is going to look like this \ so start at 12 and go down four. (0,8) then to the right one. (1,8) and that would be another point on your line.

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Answer:

Step-by-step explanation:

The average rate of change is the slope. However, since this is not a linear function but an exponential one, we cannot determine the slope of the function, only the slope of the secant line that connects the x-values of 4 and 8. In order to do that we need to find the corresponding y-coordinate that goes with each of those x-values and plug them into the slope function. What we will get is a very loose interpretation of the rate of change of population, but that's all we have short of using calculus. It would be a closer estimation if we looked at x values of 4 and 5, or eve 4 ad 4.5. But that's not what we're being asked. So let's get to it.

Sub first 4 in for x and then 8, to get each y value:

$P(4)=2560e^{(.017185)(4)}$ to get that P(4) = 2742.16

$P(8)=2560e^{(.017185)(8)}$ to get that P(8) = 2937.29

The coordinates for these are (4, 2742.16) and (8, 2937.29)

Plug into the slope formula:

$m=\frac{2937.29-2742.16}{8-4}$ which gives you, in decimal form rounded to the nearest hundredth,

48.78 million.

The interpretation of this value in our situation is that between 1954 and 1958 the population increased 48.78 million people per year.

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