Sort the data by x:
(26,31),(29,28), (33,25), (38,21),(45,18),(49,17),(55,15), (62,13),(64,13), (72,11), (92,9)}
That look like an obvious decreasing trend. From the first and last point we get a slope of (9-31)/(92-26) = -1/3 and a y intercept of 31 - (-1/3)26 = 39.67.
That's pretty close to Choice d y=-3/10x+35
Answer: d
Answer:
0.2071
Step-by-step explanation:
It looks like the graph is of the function ...
y = √(x +8) -2
We know that (-4, 0) is one point on the graph. The other point of interest is at x=0, where y = √8 -2 ≈ 0.8284.
The average rate of change on the interval is then ...
m = (0.8284 -0)/(0 -(-4)) = 0.2071
The average rate of change on the interval is about 0.2071.
_____
<em>Rougher estimate</em>
The graph goes through the points (-4, 0) and (1, 1), so has a slope of 1/5 = 0.2 on the interval [-4, 1]. We know the graph does not go through (0, 1), so the slope is not as high as 1/4 = 0.25. The curve is concave downward, so the average slope will be higher than 0.2, but we aren't sure how much higher.
A reasonable estimate of the rate of change on the interval is "a little more than 0.2, but less than 0.25."
The amount needed in the account when Frost retires is given by the annuity formula. Compounding is 2 times per year.
.. A = Pi/(n(1 -(1 +r/n)^(-nt)))
.. 17900 = P*.08/(2*(1 -(1 +.08/2)^(-2*12)))
.. 17900 = P*.04/(1 -(1.04^-24))
.. P ≈ 272,920.64
The compound interest formula can be used to find the present value required. 4015 days is 11 years (ignoring leap years), so the amount to deposit can be calculated from
.. A = P*(1 +r/n)^(nt)
.. 272,920.64 = P*(1 +.08/2)^(2*11) = P*1.04^22
.. P ≈ 115,160.33
We don't know about the company's obligation to Robert. To fulfill its obligation to Frost, it must deposit 115,160.33 today.