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Name:
Date:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
1. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces
previous height. Find the height the ball will bounce after hitting the ground the fourth time.
(SHOW WORK)
the
Initial height – 16 feet
First bounce = 16(3/5) = 9.6 feet
Second bounce = 16(3/5)(3/5) = 5.76 feet
Third bounce = 16(3/5)(3/5)(3/5) = 3.456 feet
Fourth bounce = 16(3/5)(3/5)(3/5)(3/5) = 2.0736 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)
70𝐼
Denali: 𝑀 = log (
𝐼
) + 6.7 = log(70) + 6.7 = 1.84 + 6.7 = 8.55
30𝐼
Rat Island: 𝑀 = log (
𝐼
) + 7.8 = log(30) + 7.8 = 1.478 + 7.8 = 9.28
The building that can withstand 30 times the Rat Island earthquake is the stronger
building because it has a higher value on the Richter Scale.
Name:
Date:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
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 then the sale of motorcycles.
(SHOW WORK)
Motorcycle sales: 5.75 ∗ (1.16)𝑡
Car sales: 3.5 ∗ (1.25)𝑡
Cars > Motorcycles:
3.5(1.25)𝑡 > 5.75(1.16)𝑡
1.16 𝑡
)
0.61 > (
1.25
1.16
)
ln(0.61) > 𝑡 ∗ ln (
1.25
−0.49 > 𝑡 ∗ (−0.07)
𝑡>7
In 7 years the car sales will exceed the motorcycle sales.
Name:
Date:
Algebra 2 Part 2 Final Exam
Directions: Answer the questions below. Make sure to show your work and justify all your
answers.
In a survey in 2010, the population of two plant species were found to be gr...