Performance Task: Make Your Money Work for You 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 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?

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

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?

Food poisoning occurs when bacteria like Salmonella and Listeria grow on food. These microorganisms grow at an exponential rate. When an initial population of 100 bacteria are left at , they will grow at a rate of . Which graph could be used to calculate the number of bacteria after a certain number of hours?

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?

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 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?

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

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

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

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 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?

Food poisoning occurs when bacteria like Salmonella and Listeria grow on food. These microorganisms grow at an exponential rate. When an initial population of 100 bacteria are left at , they will grow at a rate of . Which graph could be used to calculate the number of bacteria after a certain number of hours?

Which point corresponds to the real zero of the graph of ?

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?

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?

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

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 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?

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?