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Shawn Numerade

Shawn N.

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Viewed Questions

Explain how to convert an exponential expression $b^{t}$ to an exponential expression base $e$.

Explain how to convert an exponential expression $b^{t}$ to an exponential expression base $e$.

College Algebra Essentials

Exponential and Logarithmic Functions

Modeling with Exponential and…
After a new product is launched the cumulative sales $S(t)$ (in $\$ 1000) t$ weeks after launch is given by: $$S(t)=\frac{72}{1+9 e^{-0.36 t}}$$ a. Determine the cumulative amount in sales 3 weeks after launch. Round to the nearest thousand. b. Determine the amount of time required for the cumulative sales to reach $\$ 70,000$. c. What is the limiting value in sales?

After a new product is launched the cumulative sales $S(t)$ (in $\$ 1000) t$ weeks after launch is given by: $$S(t)=\frac{72}{1+9 e^{-0.36 t}}$$ a. Determine the cumulative amount in sales 3 weeks after launch. Round to the nearest thousand. b. Determine the amount of time required for the cumulative sales to reach $\$ 70,000$. c. What is the limiting value in sales?

College Algebra Essentials

Exponential and Logarithmic Functions

Modeling with Exponential and…
Technetium- $99\left({ }^{99 \mathrm{~m}} \mathrm{Tc}\right)$ is a radionuclide used widely in nuclear medicine. ${ }^{99 \mathrm{~m}} \mathrm{Tc}$ is combined with another substance that is readily absorbed by a targeted body organ. Then, special cameras sensitive to the gamma rays emitted by the technetium are used to record pictures of the organ. Suppose that a technician prepares a sample of $^{99 \mathrm{~m}}$ Tc-pyrophosphate to image the heart of a patient suspected of having had a mild heart attack. a. At noon, the patient is given $10 \mathrm{mCi}$ (millicuries) of ${ }^{99 \mathrm{~m}} \mathrm{Tc}$. If the half-life of ${ }^{99 \mathrm{~m}} \mathrm{Tc}$ is $6 \mathrm{hr}$, write a function of the form $Q(t)=Q_{0} e^{-k t}$ to model the radioactivity level $Q(t)$ after $t$ hours. b. At what time will the level of radioactivity reach $3 \mathrm{mCi} ?$ Round to 1 decimal place.

Technetium- $99\left({ }^{99 \mathrm{~m}} \mathrm{Tc}\right)$ is a radionuclide used widely in nuclear medicine. ${ }^{99 \mathrm{~m}} \mathrm{Tc}$ is combined with another substance that is readily absorbed by a targeted body organ. Then, special cameras sensitive to the gamma rays emitted by the technetium are used to record pictures of the organ. Suppose that a technician prepares a sample of $^{99 \mathrm{~m}}$ Tc-pyrophosphate to image the heart of a patient suspected of having had a mild heart attack. a. At noon, the patient is given $10 \mathrm{mCi}$ (millicuries) of ${ }^{99 \mathrm{~m}} \mathrm{Tc}$. If the half-life of ${ }^{99 \mathrm{~m}} \mathrm{Tc}$ is $6 \mathrm{hr}$, write a function of the form $Q(t)=Q_{0} e^{-k t}$ to model the radioactivity level $Q(t)$ after $t$ hours. b. At what time will the level of radioactivity reach $3 \mathrm{mCi} ?$ Round to 1 decimal place.

College Algebra Essentials

Exponential and Logarithmic Functions

Modeling with Exponential and…
$^{99 \text { m }}$Tc is a radionuclide of technetium that is widely used in nuclear medicine. Although its half-life is only 6 hr, the isotope is continuously produced via the decay of its longer-lived parent $^{99}$Mo (molybdenum 99) whose half-life is approximately 3 days. The $^{99}$Mo generators (or "cows") are sold to hospitals in which the $^{99 \text { m }}$Tc can be "milked" as needed over a period of a few weeks. Once separated from its parent, the $^{99 \text { m }}$Tc may be chemically incorporated into a variety of imaging agents, each of which is designed to be taken up by a specific target organ within the body. Special cameras, sensitive to the gamma rays emitted by the technetium, are then used to record a "picture" (similar in appearance to an X-ray film) of the selected organ. Suppose a technician prepares a sample of $^{99 \text { m }}$Tc-pyrophosphate to image the heart of a patient suspected of having had a mild heart attack. If the injection contains 10 millicuries ( $\mathrm{mCi}$ ) of $^{99 \text { m }}$Tc at 1: 00 P.M., then the amount of technetium still present is given by $$T(t)=10 e^{-0.1155 t}$$ where $t>0$ represents the time in hours after 1: 00 P.M. and $T(t)$ represents the amount of $^{99 \mathrm{m}} \mathrm{Tc}$ (in millicuries) still present. a. How many millicuries of $^{99 \mathrm{m}}$ Tc will remain at 4: 20 P.M. when the image is recorded? Round to the nearest tenth of a millicurie. b. How long will it take for the radioactive level of the $^{99 \mathrm{m}}$ Te to reach $2 \mathrm{mCi}$ ? Round to the nearest tenth of an hour.

$^{99 \text { m }}$Tc is a radionuclide of technetium that is widely used in nuclear medicine. Although its half-life is only 6 hr, the isotope is continuously produced via the decay of its longer-lived parent $^{99}$Mo (molybdenum 99) whose half-life is approximately 3 days. The $^{99}$Mo generators (or "cows") are sold to hospitals in which the $^{99 \text { m }}$Tc can be "milked" as needed over a period of a few weeks. Once separated from its parent, the $^{99 \text { m }}$Tc may be chemically incorporated into a variety of imaging agents, each of which is designed to be taken up by a specific target organ within the body. Special cameras, sensitive to the gamma rays emitted by the technetium, are then used to record a "picture" (similar in appearance to an X-ray film) of the selected organ. Suppose a technician prepares a sample of $^{99 \text { m }}$Tc-pyrophosphate to image the heart of a patient suspected of having had a mild heart attack. If the injection contains 10 millicuries ( $\mathrm{mCi}$ ) of $^{99 \text { m }}$Tc at 1: 00 P.M., then the amount of technetium still present is given by $$T(t)=10 e^{-0.1155 t}$$ where $t>0$ represents the time in hours after 1: 00 P.M. and $T(t)$ represents the amount of $^{99 \mathrm{m}} \mathrm{Tc}$ (in millicuries) still present. a. How many millicuries of $^{99 \mathrm{m}}$ Tc will remain at 4: 20 P.M. when the image is recorded? Round to the nearest tenth of a millicurie. b. How long will it take for the radioactive level of the $^{99 \mathrm{m}}$ Te to reach $2 \mathrm{mCi}$ ? Round to the nearest tenth of an hour.

Beginning and Intermediate Algebra

Exponential and Logarithmic Functions…

Logarithmic and Exponential Equations…

Questions asked

ANSWERED

Yujie Wang verified

Numerade educator

4ln5-6ln3

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