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Strontium-90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium-90 is left after 20 years? (c) When will only 600 grams of strontium-90 be left? (d) What is the half-life of strontium-90? (a) The decay rate of strontium-90 is %. (b) Approximately grams of strontium-90 is left after 20 years. (c) Only 600 grams of strontium-90 will be left in about years. (d) The half-life of strontium-90 is approximately years. 

          Strontium-90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90.
(a) What is the decay rate of strontium-90?
(b) How much strontium-90 is left after 20 years?
(c) When will only 600 grams of strontium-90 be left?
(d) What is the half-life of strontium-90?
(a) The decay rate of strontium-90 is %.
(b) Approximately grams of strontium-90 is left after 20 years.
(c) Only 600 grams of strontium-90 will be left in about years.
(d) The half-life of strontium-90 is approximately years.
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Strontium-90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium-90 is left after 20 years? (c) When will only 600 grams of strontium-90 be left? (d) What is the half-life of strontium-90? (a) The decay rate of strontium-90 is %. (b) Approximately grams of strontium-90 is left after 20 years. (c) Only 600 grams of strontium-90 will be left in about years. (d) The half-life of strontium-90 is approximately years.

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Strontium-90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium-90 is left after 20 years? (c) When will only 600 grams of strontium-90 be left? (d) What is the half-life of strontium-90? (a) The decay rate of strontium-90 is %. (b) Approximately grams of strontium-90 is left after 20 years. (c) Only 600 grams of strontium-90 will be left in about years. (d) The half-life of strontium-90 is approximately years.
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Strontium-90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium-90 is left after 20 years? (c) When will only 600 grams of strontium-90 be left? (d) What is the half-life of strontium-90? (a) The decay rate of strontium-90 is %. (b) Approximately grams of strontium-90 is left after 20 years. (c) Only 600 grams of strontium-90 will be left in about years. (d) The half-life of strontium-90 is approximately years.

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Strontium 90 is a radioactive material that decays according to the function A(t) = A0 e^-0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium 90. (a) What is the decay rate of strontium 90? (b) How much strontium 90 is left after 40 years? (c) When will only 100 grams of strontium 90 be left? (d) What is the half-life of strontium 90? (a) What is the decay rate of strontium 90? % (Type an integer or a decimal. Include the negative sign for the decay rate.)

Nicole H.
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Radioactive Decay Strontium-90 is a radioactive material that decays according to the function $A(t)=A_{0} e^{-0.0244 t}$ where $A_{0}$ is the initial amount present and $A$ is the amount present at time $t$ (in years). Assume that a scientist has a sample of 500 grams of strontium-90. (a) What is the decay rate of strontium-90? (b) How much strontium- 90 is left after 10 years? (c) When will 400 grams of strontium-90 be left? (d) What is the half-life of strontium-90?

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Transcript

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00:01 So in this problem, we're working with a radioactive substance called strontium 90.
00:10 And we're told that it follows this exponential decay formula.
00:16 A of t, the amount after time t, is equal to the initial amount e to negative 0 .0244t, where t is in years.
00:33 We're told that a scientist initially has 400 grams.
00:41 We're first asked, what's the decay rate? all right, so to find the decay rate, we've got to look at this exponential right here.
00:57 So e to the negative 0 .044 is what? we'll go to our calculator.
01:05 0244 negative, take e to that number, and that is 0 .0244 is 0 .0244 is 0 .4 .244 .5.
01:11 0 .9759.
01:18 So to find the decay rate, we go 1 minus this number, 0 .9759, and that gives us a decay rate of 0 .0241.
01:35 So that means 2 .41 percent.
01:41 Decay.
01:42 There's our decay rate.
01:45 Okay.
01:46 Now then, we're next asked, after 10 years, how much does he have left? so a of 10 is 400 e to the minus 0 .0244 times 10.
02:11 So 0244 times 10 negative, e to that exponent times 400 is 313 .4 grams.
02:30 That out.
02:34 All right.
02:35 Then we're next asked, how long till we get to 100 grams? all right, so we set it up, right? so it's 100 grams.
02:48 It's 400 grams, because we started at 400, e to the amount of 0 .044t...
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