Exam 5: Trigonometric Functions: Right Triangle Approach

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. $f ( x ) = 2 ^ { x } , f ( 0.5 ) , f ( \sqrt { 2 } ) , f ( \pi ) , f ( 1 / 3 )$

Find the decibel intensity level at a crowded football game if the intensity was measured at $3.98 \times 10 ^ { - 3 }$ $\text{ watts/m}^2$

Write the equation in logarithmic form. $81 ^ { - 1 / 2 } = 1 / 9$

A substance has a hydrogen ion concentration of $\left[ \mathrm { H } ^ { +} \right] = 4.0 \times 10 ^ { - 3 }$ M. Find the pH of the substance

The velocity of a sky diver t seconds after jumping is given by $v ( t ) = 80 \left( 1 - e ^ { - 02 t } \right)$ . After how many seconds is the velocity 50 ft/s?

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

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

Approximately how long will it take an investment of $\$ 300$ to triple, if the interest rate is $3.5 \%$ Per year compounded continuously?

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

The time required to double the amount of an investment at an interest rate r compounded continuously is given by $t = \frac { \ln 2 } { r }$ Find the time required to double an investment at 4%, 5%, and 6%.

Find the decibel intensity level at a crowded football game if the intensity was measured at $3.98 \times 10 ^ { - 3 }$$\text{ watts/m}^2$

The age of an ancient artifact can be determined by the amount of radioactive carbon-14 remaining in it. If $D _ { 0 }$ is the original amount of carbon-14 and D is the amount remaining, then the artifact's age A (in years) is given by $A = - 8267 \ln \left( \frac { D } { D _ { 0 } } \right)$ Find the age of an object if the amount D of carbon-14 that remains in the object is 50% of the original amount $D _ { 0 }$

Loren wants to invest $\$ 6,500$ in a fund at an interest rate of $7.5 \%$ Per year, compounded monthly. How long will it take her investment to grow to $\$ 7,850 ?$

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

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

Use a graphing device to find the solutions of the equation, correct to two decimal places. $3 \ln x = 6 - 2 x$

Find the domain, range, and asymptote if any. $h ( x ) = e ^ { x + 1 } - 5$

Solve the inequality: $\frac { 1 } { 3 } \leq \log x < 1$

Use a graphing device to find the solutions of the equation, correct to two decimal places. $9 - x ^ { 2 } = e ^ { - 3 x }$

Solve the equation. Find the exact solution. $x ^ { 2 } e ^ { 2 x } - 5 x e ^ { 2 x } = - 6 e ^ { 2 x }$