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Math 1320 Name D.Wilson
Exam #2 Review
This review packet is due on the day of Exam #2. Please also study the quizzes, group work, notes, and past WebAssign homeworks.
- A sample of radioactive material weighs 10 mg. There are 6 mg left after 28 years.
(a) Find the exponential model y = Abt^ that gives the weight of the material after t years.
(b) What is the material’s half-life? Include the units in the answer.
- A radioactive substance has a half-life of 65 years. A lab originally had 20 grams of the substance.
(a) Find the exponential model y = Abt^ that gives the weight of the material after t years.
(b) How much of the sample was left after 20 years? Include the units in the answer.
- There are 5,750 bacteria in a petri dish. Two hours later, there are 7,500 bacteria.
(a) Find the exponential model y = Abt^ that gives the number of bacteria in the dish after t hours.
(b) When will there be 10,000 bacteria in the dish? Include the units in the answer.
- Use either the substitution or elimination method to solve the systems. Show all work.
x 2 −^
y x^4 =^1 4 +^ y^ =^ −^4
7. Solve for x. Round all answers to four decimal places.
- (a) 4 ln(x^3 − 5) =
- (b) 6 + 21e4+11x =
- (c) 21 log 2 (9 − 4 x) − 13 =
- (d) 75 − 34 x−^6 =
- For each system: define the variables; set up the equations; and solve by using a graphing calculator.
(a) Ralph has three bonds earning 6%, 8%, and 12% annual interest. The amount invested at 8% is $5,000 more than the amount invested at 6%. The total yearly interest on the three bonds is $1,880. If the total amount invested is $19,000, what is the amount invested at each rate?
(b) A lawnmower equipment manufacturer makes three types of riding mowers: Types A, B, and C. Restrictions on supplies force the company to produce 10 units more of Type C than the total of the other two types, and twice as many Type B mowers as Type A mowers. The company must produce 490 mowers per month. How many of each type of mower should they produce?
(c) A box contains $8.45 in nickels, dimes, and quarters. There are 70 coins in all, and the sum of the numbers of dimes and quarters is 26 more than the number of nickels. How many nickels, dimes and quarters are there?
F V = P M T
[
(1 + i)n^ − 1 i
]
and P V = P M T
[
1 − (1 + i)−n i
]
- (a) Martin has $9,500 in his savings account, which earns 2.5% annual interest, compounded weekly. He needs $18,000 to buy a new car in 18 months. What weekly deposit should he make in order to attain his savings goal?
(b) Jeremy has $45,000 in a fund that earns 6% annual interest, compounded every two months. Determine the deposits he has to make every two months in order to have $1,500,000 in the fund in 20 years.
(c) The Smiths just purchased a home worth $125,000. They made an $8,000 downpayment, and took out a 30-year loan (mortgage) on the balance. The annual interest on the mortgage is 5.78%, compounded monthly.
- What is the amount of the Smiths’ loan?
- What is the Smiths’ monthly payment?
- Including the $8,000 downpayment, what is the total amount that the Smiths will pay for their home after 30 years?
- How much interest will the Smiths have paid?
