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Jb Algebra 2 Questions

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1. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces the
previous height. Find the height the ball will bounce after hitting the ground the fourth time.
(SHOW WORK)
Each time the ball hits the ground requires a separate factor of 3/5, so the final height of the ball is:
(16 feet)*(3/5) *(3/5) *(3/5) *(3/5) = (16)(81) / (25)(25) = 2.07 feet
2. The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7. The 2003 Rat Islands
earthquake in Alaska had a Richter scale magnitude of 7.8.
(SHOW WORK)
Suppose an architect has designed a building strong enough to withstand an earthquake 70 times as
intense as the Denali quake and 30 times as intense as the Rat Islands quake. Find which structure is
strongest. Explain your finding.
(SHOW WORK)
??????
This question (#2) appears to be missing information about a second structure, which is referred to
in the problem.

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3. Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The
growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the
sale of cars will be more than the sale of motorcycles.
(SHOW WORK)
Factors of 1.16 and 1.25 can be used here to calculate the growth in sales of motorcycles and cars,
respectively. Let t = the time when sales of cars and motorcycles will be equal.
(5.75 million motorcycles)*(1.16)^t = (3.5 million cars)*(1.25)^t
(1.16)^t = (3.5 million cars)_________
(1.25)^t (5.75 million motorcycles)
log (1.16)^t = log (3.5 million cars)_______
(1.25)^t (5.75 million motorcycles)
log (1.16)^t - log (1.25)^t = log (3.5 / 5.75)
t * log (1.16) - t*log (1.25) = - 0.2156
t * ( log 1.16 log 1.25) = - 0.2156
t * -0.03245 = - 0.2156
t = - 0.2156 / -0.03245
t = 6.644
Sales of motorcycles and cars will be equal after about 6.644 yearly increases in sales, so sales of cars
will surpass sales of motorcycles after:
6 years and (0.644)*(12 months)
= 6 years and about 8 months, in August of year 2016.

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1. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces the previous height. Find the height the ball will bounce after hitting the ground the fourth time. (SHOW WORK) Each time the ball hits the ground requires a separate factor of 3/5, so the final height of the ball is: (16 feet)*(3/5) *(3/5) *(3/5) *(3/5) = (16)(81) / (25)(25) = 2.07 feet 2. The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7. The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8. (SHOW WORK) Suppose an architect has designed a building strong enough to withstand an earthquake 70 times as intense as the Denali quake and 30 times as intense as the Rat Islands quake. Find which structure is strongest. Explain your finding. (SHOW WORK) ?????? This question (#2) appears to be missing information about a second structure, which is referred to in the problem. 3. Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the sale of cars will be more than the sale of motorcycles. (SHOW WORK) Factors of 1.16 and 1.25 can be used here to calculate the growth in sales of motorcycles and cars, respectively. Let t = the time when sales of cars and motorcycles will be equal. (5.75 million motorcycles)*(1.16)^t = (3.5 million cars)*(1.25)^t (1.16)^t = (1.25)^t log (1.16)^t (1.25)^t (3.5 mill ...
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I was struggling with this subject, and this helped me a ton!

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