MATH Precalculus

1) A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 26 hours, 75 mg of the substance remains. How many milligrams will remain after 46 hours?

2) A house was valued at $110,000 in the year 1988. The value appreciated to $155,000 by the year 2004.

A) What was the annual growth rate between 1988 and 2004?
r = ??? Round the growth rate to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r = %.

C) Assume that the house value continues to grow by the same percentage. What will the value equal in the year 2009 ?
value = $? Round to the nearest thousand dollars.

  1. 👍
  2. 👎
  3. 👁
  1. let amount = c e^(kt), where c is the starting amount, and t is in hours, and k is a constant.
    In our case c = 150

    given: when t = 26, amount = 75
    75 = 150 e^(26k)
    .5 = e^(26k)
    26k lne = ln .5
    26k (1) = ln .5
    k = ln .5/26 = appr -.0266595

    then:
    amount = 150 e^(-.266595t)
    so for t = 46
    amount = 150 e^-1.2263373
    = 44.005 mg

    Use the same method for #2

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (b) How long would it take the sample to decay to

  2. precalculus

    Twenty percent of a radioactive substance decays in ten years. By what percent does the substance decay each year?

  3. Science- Radioactive Dating

    Which of the following statements about radioactive dating is true? a. Radioactive decay is the rate at which new atoms form. b. During radioactive decay, atoms break down, releasing particles or energy. c. The rate of decay of a

  4. Intergrated Science A

    Which answer choices best indicate that a substance has experienced a chemical change? Select all that apply. when the substance changes temperature when the substance changes shape when the substance changes volume when a new

  1. Calc

    A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years

  2. Math

    A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a

  3. Calculus-Modeling Equations

    An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent. 1.What is the half-life of the element? 2.How long will it take for a sample of 100 mg to

  4. Math

    A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactive substance. After 20 hours, 65 mg of the substance remains. How many milligrams will remain after 24 hours?

  1. Exponential Modeling

    The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance. How many grams of the substance would be left after a week?

  2. algebra

    A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The half-life of the substance is 10

  3. Calculus

    A certain radioactive material decays exponetially. The percent, P, of the material left after t years is given by P(t)= 100(1.2)^-t a)Determine the half life of the substance

  4. calculus

    The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram

You can view more similar questions or ask a new question.