Exam 11: Exponential and Logarithmic Functions

Suppose that a certain radioactive substance has a half-life of 45 years. If there are presently 1,920 milligrams of the substance, how much, to the nearest milligram, will remain after 180 years?

Solve the equation. $\log _ { 27 } x = \frac { 4 } { 3 }$

A principal sum of money P is invested at the end of each year in an annuity earning annual interest at a rate of r . The amount in the annuity account will be A dollars after n years, where $n = \frac { \log \left( \frac { A v } { P } + 1 \right) } { \log ( 1 + r ) }$ If $2,000 is invested each year in an annuity earning 9% annual interest, how long will it take for the account to be worth $15,000? Round the answer to the nearest tenth of the year.

Use your calculator to find x when given ln x . Express answer to four decimal places. $\ln x = 0.5973$

Use your calculator to find x when given ln x . Express answer to four decimal places. $\ln x = - 2.2449$

Find the value of $x$ . $\log _ { 81 } x = \frac { 1 } { 2 }$

Calculate how many times more intense an earthquake with a Richter number of 8.3 is than an earthquake with a Richter number of 6.9. Please round the answer to the whole number.

Business equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing C dollars, will depreciate to a value of V dollars in n years, where n is given by the formula: $n = \frac { \log V - \log C } { \log \left( 1 - \frac { 2 } { N } \right) }$ A computer that cost $10,000 has a life expectancy of 5 years. If it has depreciated to a value of $2,000, how old is it? Round the answer to the nearest tenth of the year.

Evaluate the expression log ₉ (log ₂ 8).

Graph the exponential function. f ( x )= 3 ^x

Solve the exponential equation and express solution to the nearest hundredth. $2 e ^ { x } = 28.8$

Solve the equation. $\left( \frac { 1 } { 5 } \right) ^ { 2 x } = 625$

Write the following equation in logarithmic form. For example, 2 ³ = 8 becomes log ₂ 8 = 3 in logarithmic form. $2 ^ { - 5 } = \frac { 1 } { 32 }$

Solve the equation. $\left( 4 ^ { 3 x - 6 } \right) \left( 4 ^ { x + 4 } \right) = 64$

Solve the logarithmic equation. Check the solution. $\log x ^ { 3 } = 9$

Complete the following chart, which illustrates what happens to $16,000 invested at various rates of interest for different lengths of time but always compounded continuously. Round your answers to the nearest dollar. \% \% \% \% 5 years 8 years 11 years 14 years 17 years

The number of bacteria present at a given time under certain conditions is given by the equation Q = 4,000 e ^{0.01 t} , where t is expressed in minutes. How many bacteria are present at the end of 45 minutes? Please round the answers to the nearest whole.

Suppose that Nora invested $400 at 8.5% compounded annually for 6 years and Patti invested $400 at 8% compounded quarterly for 6 years. At the end of 6 years, who will have the most money and by how much (to the nearest dollar)?

An earthquake in the Japan in 2011 was about 10 9 times as intense as the reference intensity. Find the Richter number for that earthquake. NOTE: Seismologists use the Richter scale to measure and report the magnitude of earthquakes. The equation $R = \log \frac { I } { I _ { 0 } }$ compares the intensity I of an earthquake to a minimum or reference intensity I 0.

Complete the following chart, which illustrates what happens to $8,000 invested at 12% for different lengths of time and different numbers of compounding periods. Round all of your answers to the nearest dollar. l year T years 14 years 28 years Compounded annually Compoundedsemiannually Compounded quatterly Compounded monthly Compounded continuously