Modeling with Exponential and Logarithmic Equations Answers

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 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?

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 ?

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?

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?

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?

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in 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

The magnitude of an earthquake, R, can be measured by the equation , where A is the amplitude in micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter. If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?

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. Which equation models the concentration of hydrogen ions (H+) of a solution whose pH is 7.2?

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