Modeling with Exponential and Logarithmic Equations Answers

Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution whose hydrogen ion concentration is ?

Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of organisms after y years. y yearsnumber of organisms, n155260367475The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?

The estimated number of organisms in a population after t days is shown in the table below.t daysestimated number of organisms, n286041,25061,80082,600103,720Which equation best models the situation?

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?M = the magnitude of an earthquakeI = the intensity of an earthquakeI0 = the smallest seismic activity that can be measured, which is 1

When Akbar’s son was four years old, Akbar put $250 into an account that guaranteed a 10% annual return. The equation represents the amount of money in the account when the child will be x years old.Which graph models the scenario?

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?

A pizza is taken out of an oven and placed on a counter. The temperature, T, in degrees Fahrenheit, of the pizza after m minutes is modeled by the function . Which graph represents the model?

A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?

The general equation for depreciation is given by y = A(1 – r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. A car was purchased 6 years ago for $25,000. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?

Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. What is the annual interest rate of the account?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

How would you describe the relationship between the real zeros and x-intercepts of the function ?

The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10-mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains?

The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?L = loudness, in decibelsI = sound intensity, in watts/m2I0 = 10–12 watts/m2

The pH of a particular solution is given by , where x represents the concentration of the hydrogen ions in the solution, in moles per liter. Which graph models the pH of this solution?