Question

The isotope of plutonium $^{238}Pu$ is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of $^{238}Pu$. (a) If the half-life of $^{238}Pu$ is 87.7 yr, write a function of the form $Q(t) = Q_0e^{-kt}$ to model the quantity $Q(t)$ of $^{238}Pu$ left after $t$ years. Round the value of $k$ to five decimal places. Do not round intermediate calculations. $Q(t) = \boxed{}$

Name: the isotope of plutonium 238pu is used to make thermoelectric power sources for spacecraft suppose that a space probe was launched in 2012 with 40 kg of 238pu a if the half life of 238pu is 01945
Uploaded: 2022-01-18T16:13:12-08:00
Duration: 1 min 42 s
Channel: Victor Salazar
Description: the isotope of plutonium 238pu is used to make thermoelectric power sources for spacecraft suppose that a space probe was launched in 2012 with 40 kg of 238pu a if the half life of 238pu is 01945

          The isotope of plutonium $^{238}Pu$ is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of $^{238}Pu$.
(a) If the half-life of $^{238}Pu$ is 87.7 yr, write a function of the form $Q(t) = Q_0e^{-kt}$ to model the quantity $Q(t)$ of $^{238}Pu$ left after $t$ years. Round the value of $k$ to five decimal places. Do not round intermediate calculations.
$Q(t) = \boxed{}$

the isotope of plutonium 238pu is used to make thermoelectric power sources for spacecraft suppose that a space probe was launched in 2012 with 40 kg of 238pu a if the half life of 238pu is 01945

Added by Aitor T.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Victor Salazar

01/18/2022

Step 1

The half-life is the time it takes for the quantity to reduce to half its initial value. In this case, the half-life is 87.7 years. So, when $t = 87.7$, $Q(t) = \frac{1}{2}Q_0$. Substituting these values into the formula, we get: $\frac{1}{2}Q_0 = Show more…

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The isotope of plutonium $^{238}Pu$ is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of $^{238}Pu$. (a) If the half-life of $^{238}Pu$ is 87.7 yr, write a function of the form $Q(t) = Q_0e^{-kt}$ to model the quantity $Q(t)$ of $^{238}Pu$ left after $t$ years. Round the value of $k$ to five decimal places. Do not round intermediate calculations. $Q(t) = \boxed{}$