Speed Boat Designs
y=ab^x???? could someone plz help me with these 3 questions and go step by step with the answers. im lost?
1. a particular class of singlenegine boats has a hull design that allows a top speed, s, in knots, that depends on the horsepower, p, develop[ed by the boat’s engine, with s=20.8p^1/6 . a. if one of these boats has a 145 horsepower engine, what is its top speed? b. if the top speed of one of these boats is 65 knots, what is the horsepower of its engine?
2. in the US a pound of a particular brand of chocolate candy costs ana verage of $10.59 today. if the average cost was 7.89 five years ago, what is the inflation rate? hint find the ratio first.
3. consider and exponential function that passes thru the points (4,50) and (5,36).
a. write an equation for this function in point ratio form.
1a. Plug the information provided into the equation and solve.
s=20.8p^(1/6) the problem provides that p = 145 hp
s=20.8*145^(1/6)
s=20.8*2.29
s=47.68
Top speed is 47.68 knots
1b. Plug the information provided into the equation and solve
s=20.8p^(1/6) the problem provides that s = 65 knots
65 = 20.8p^(1/6)
65/20.8 = p^(1/6)
3.125 = p^(1/6)
3.125^6=p
931.322 = p
The horsepower developed by the engine is 931.322 hp.
2. 10.59-7.89 = $2.70 = The change in price over 5 years
$2.70/5 = $0.59 = The average change in price each year
3. y=mx+b where m = slope of the line and b = a constant for that particular line.
m = change in y over the change in x (rise over run) = (50-36)/(4-5) = -14 it doesn’t matter which point you use first just as long as you are consistent through the equation.
(36-50)/(5-4) = -14
so m = -14
y=-14x+b
use one of the points provided to solve for b.
y=-14x+b using (4,50)
50=-14(4)+b
50 = -56+b
50+56 = b
106 = b
The equation is y=-14x+106
To check use the other point and see if it solves correctly
y=-14x+106 using x=5 from (5,36)
y=-14(5)+106
y=-70+106
y=-36
The equation works! it is correct.
Hope this helps -b
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