Exam 5: Trigonometric Functions: Right Triangle Approach

If $10,000 is invested in an account at 5% per year, find the amount of the investment at the end of 12 years for the following compounding methods a)Continuously b) Daily

A certain strain of bacteria divides every three hours. If a colony is started with 50 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by $t = 3 \frac { \log ( N / 50 ) } { \log 2 }$ Find the time required for the colony to grow to five million bacteria.

Evaluate the expression without using a calculator. $\log _ { 7 } ( \sqrt { 7 } )$

Solve the equation. Find the exact solution. $\log x + \log ( x + 1 ) = \log 20$

Write the equation in logarithmic form. $25 ^ { - 1 / 2 } = \frac { 1 } { 5 }$

Expand the logarithmic expression. $\log \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

Evaluate the expression without using a calculator. $\log _ { 2 } 16 ^ { 23 }$

Combine into a single logarithm. $\log _ { 2 } x + \log _ { 2 } \left( x y ^ { 2 } \right) + 4 \log _ { 2 } y$

Evaluate the expression without using a calculator. $\log 50 + \log 2$

Radium - $226$ has a half-life of $1600 \text { years }$ . Suppose we have a $300 \mathrm {~g}$ sample. (a) Find a formula for the mass remaining after ${ t }$ years b) How much of the sample remains after $200$ years? c) After how long will only $20 \mathrm {~g}$ remain?

How much more intense is an earthquake with a magnitude of $9.5$ on the Richter scale than one with a magnitude of $7.6$ ?

A culture contains $680$ bacteria. After just $30$ Minutes, the count is $3250$ ) Find the number of bacteria after $3.5$ Hours

A culture contains $680$ bacteria. After just $30$ minutes the count is $3250$ . Find the number of bacteria after $3.5$ hours. After how many minutes will the number of bacteria triple?

Solve the equation. Find the exact solution. $e^{3 x / 5}=7$

Brian wants to invest $\$ 6,500$ at an interest rate of $7.5 \%$ Per year, compounded daily. How long will it take his investment to grow to $\$ 8,000 ?$

How much more intense is an earthquake with a magnitude of $5.4$ on the Richter scale than one with a magnitude of $3.2$ ?

Expand the logarithmic expression. $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

Sketch the graph of the function. $f ( x ) = 3 + 3 ^ { x }$

How long will it take an investment of $\$ 300$ to triple, if the interest rate is $9.5 \%$ per year compounded continuously?

Find the domain of the function. $h ( x ) = \ln \left( x ^ { 2 } - 9 \right)$