Math 4 Final Exam Review 4

The graph of $y = 2 \log_{3}(x - 1) + 2$ has an asymptote of ________.

Find the balance of a $500 investment after 18 years earning 7.9% interest compounded continuously.

What interest rate is required for an investment with continuously compounded interest to double in 5 years?

Determine the amount of money in a money market account providing an annual rate of 7% compounded daily if George invested $2,500 and left it in the account for 10 years.

The half-life of radium-226 is 1,590 years.
(a) If a sample has a mass of 150 mg, find the mass that remains after 1,000 years.
(b) After how many years will only 50 mg remain?

The number of bacteria in a culture is modeled by the function $n(t) = 500e^{0.45t}$. How many bacteria are in the culture after 3 hours?

If $\angle P = 27^\circ$, $\angle R = 90^\circ$, and $r = 11$, find $p$.

The angle of elevation of a ladder leaning against a wall is $55^\circ$. The ladder is 30 feet long. How high up the wall did it reach?

In $\triangle ABC$, find $c$ if $\angle A = 36^\circ$, $\angle B = 101^\circ$, and $b = 42.7$.

In $\triangle ABC$, given $a = 22$, $b = 39$, and $c = 19$, find $B$.

Two motorists start at the same point and travel in 2 straight courses. The courses diverge by $95^\circ$. If one is traveling at 50 mph and the other is traveling at 60 mph, how far apart will they be after 4 hours?

A geologist measured a $43^\circ$ angle of elevation to the top of a volcano crater. After moving 0.25 km farther away the angle of elevation was $38^\circ$. Find the height of the volcano crater.

Find $7A + 6B$.

Solve for the missing variables in the matrix equation shown.

Juliet plans to buy a supply of blank compact discs. She checked price lists and found out that if she bought 100 CDs or less it would cost her $$0.70$ each. However, if she buys between 100 and 200 CDs, the price drops to $$0.65$ each for the second hundred. Also, for any purchase of more than 200, the price drops again to $$0.61$ for each one over 200. What is the cost for Juliet to purchase 260 compact discs?

Write a piecewise function for the pricing scenario in the previous question about Juliet buying compact discs.

f(0), $f(2)$, and $f(3)$.

A silk-screen shop charges an initial fee of $10 to create the silk screen and $8.50 per shirt for the first 25 shirts. If you decide to purchase more than 25 shirts, the price goes down to $7.75 per shirt (after the first 25 shirts are purchased). Write a function that gives the cost, $C$, for an order of $x$ shirts. How much does it cost to purchase 20 shirts? 40 shirts?

Change from logarithmic form to exponential form: $\log_{27} 9 = 2/3$.

Convert from exponential form to logarithmic form: $16^{1/2} = 4$.