Exam 3: Exponential and Logarithmic Functions

The number y of hits a new search-engine website receives each month can be modeled by $y = 4080 e ^ { k t }$ where t represents the number of months the website has been operating.In the website's third month, there were 10,000 hits.Find the value of k, and use this value to predict the number of hits the website will receive after 22 months.

Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years.Of an initial sample of 33 grams, how much will remain after 69 years? ​

Use the One-to-One Property to solve the following equation for x. $\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27$

Select the graph of the exponential function. $f ( x ) = 2 ^ { - x ^ { 2 } }$

Solve for x: $7 \left( 10 ^ { x - 3 } \right) = 23$ .Round to 3 decimal places.

Write the logarithmic equation in exponential form. $\log _ { 7 } 343 = 3$

Graph the function using translations. $f ( x ) = 3 ^ { x + 1 }$

Find the exact value of $\log _ { 4 } 44 - \log _ { 4 } 11$ without using a calculator.

Find the value of b, if any, that would cause the graph of $y = \log _ { b } x$ to look like the graph shown.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $9 + 2 \ln x = 4$

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log₉ 0.1 ​

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =256 x=2

Determine whether the given x-value is a solution (or an approximate solution) of the equation. =16 x=4

Select the correct graph for the given function $y = 5 e ^ { - ( x - 2 ) ^ { 2 } / 5 }$

A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones.The numbers of cell sites from 1985 through 2008 can be modeled by $y = \frac { 237,101 } { 1 + 1950 e ^ { - 0.355 t } }$ where t represents the year, with $t = 5$ corresponding to 1985.Use the model to find the numbers of cell sites in the year 2007 .

Solve the exponential equation algebraically.Approximate the result to three decimal places. $2 ^ { x - 5 } = 16$

Rewrite the exponential equation $4 ^ { - 2 } = \frac { 1 } { 16 }$ in logarithmic form.

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) $r = 0.0540$

Write the exponential equation $e ^ { 5 / 2 } = 12.1825 \ldots$ in logarithmic form.

Evaluate the function $f ( x ) = - 3.752 \ln x$ at $x = 4$ .Round to 3 decimal places.(You may use your calculator.)