Solve the problem.
-A nuclear scientist has a sample of 100 mg of a radioactive material which has a half-life in hours. She monitors the amount of radioactive material over a period of a day and obtains the following data. Use a graphing utility
To fit an exponential function to the data. Predict the amount of material remaining at 40 hours. $\begin{array}{l|lcccccc}
\text { Hours } & 0 & 5 & 10 & 15 & 20 & 25 & 30 \
\hline \mathrm{mg} & 100 & 68.3 & 45.2 & 31.3 & 21.5 & 14.6 & 9.8
\end{array}$
A) $\mathrm { y } = 92 \mathrm { e } ^ { - 0.0686 \mathrm { x } } , 5.9 \mathrm { mg }$
B) $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 4.6 \mathrm { mg }$
C) $\mathrm { y } = 100 \mathrm { e } ^ { - 0.077 \mathrm { x } } , 6.7 \mathrm { mg }$

Question

Quizplus · Accepted Answer

Given the data, the correct exponential function that models the decay of the radioactive material is $y = 100e^{-0.077x}$. Using this model to predict the amount of material remaining at 40 hours, we substitute $x = 40$ into the equation, resulting in approximately 4.6 mg of material remaining.

Solve the Problem A) y=92e−0.0686x,5.9mg\mathrm { y } = 92 \mathrm { e } ^ { - 0.0686 \mathrm { x } } , 5.9 \mathrm { mg }y=92e−0.0686x,5.9mg

Solve the Problem A) $\mathrm { y } = 92 \mathrm { e } ^ { - 0.0686 \mathrm { x } } , 5.9 \mathrm { mg }$