Concept explainers
For the following exercises, solve for the indicated value, and graph the situation showing the solution point.
An account with an initial deposit of
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College Algebra
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- For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. How much less would the account from Exercise 42 be worth after 30 years if it were compounded monthly instead?arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. To the nearest minute, what is the half-life of the drug?arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?arrow_forward
- For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of 12,000 earning 7.2 interest compounded continuously. How much will the account be worth after 30 years?arrow_forwardFor the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest minute, what is the half-life of this substance?arrow_forwardFor the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1,000 bacteria present after 20 minutes. Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?arrow_forward
- For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. Write an exponential model representing the amount of the drug remaining in the patient's system after t hours. Then use the formula to find the amount of the drug that would remain in the patient's system after 24 hours. Round to the nearest hundredth of a gram.arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. Write an exponential model representing the amount of the drug remaining in the patient’s system after t hours. Then use the formula to find the amount of the drug that would remain in the patient’s system after 3 hours. Round to the nearest milligram.arrow_forward
- For the following exercises, find the formula for an exponential function that passes through the two points given. (0,6) and (3,750)arrow_forwardFor the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. How much more would the account in the previous exercise have been worth if the interest were compounding weekly?arrow_forwardFor the following exercises, use the compound interest formula, A(t)=P(1+rn)nt. Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded monthly, had an initial deposit of 5,500, and was worth 38,455 after 30 years.arrow_forward