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After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly.The relationship between the elapsed time t, in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body, H_("minute ")(t), is modeled by the following function:

H_("minute ")(t)=500,000,000*(0.2)^t
Complete the following sentence about the rate of change in the number of harmful bacteria remaining in the body in seconds. Round your answer to two decimal places.
Every second, the number of harmful bacteria remaining in the body decays by a factor of◻.

After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly. The relationship between the elapsed time $t$ , in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body, $H_{\text{minute}}(t)$ , is modeled by the following function: $\newline$ $H_{\text{minute}}(t)=500,000,000*(0.2)^t$ $\newline$ Complete the following sentence about the rate of change in the number of harmful bacteria remaining in the body in seconds. $\newline$ Round your answer to two decimal places. $\newline$ Every second, the number of harmful bacteria remaining in the body decays by a factor of $\square$ .

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Find a value using two-variable equations: word problems

Full solution

Q. After a certain medicine is ingested, the number of harmful bacteria remaining in the body declines rapidly. The relationship between the elapsed time

t

, in minutes, since the medicine is ingested, and the number of harmful bacteria remaining in the body,

H_{\text{minute}}(t)

, is modeled by the following function:

\newline

H_{\text{minute}}(t)=500,000,000*(0.2)^t

\newline

Complete the following sentence about the rate of change in the number of harmful bacteria remaining in the body in seconds.

\newline

Round your answer to two decimal places.

\newline

Every second, the number of harmful bacteria remaining in the body decays by a factor of

\square

.

Convert to seconds: First, we need to convert the rate of decay from minutes to seconds since the function is given in minutes and we need the rate per second. $\newline$ There are $60$ seconds in a minute.
Calculate decay factor: Now, calculate the decay factor per second by taking the $0.2$ decay factor per minute and raising it to the power of $\frac{1}{60}$ , because there are $60$ seconds in a minute. $\newline$ $(0.2)^{\frac{1}{60}}$
Find value: Use a calculator to find the value of $(0.2)^{\frac{1}{60}}$ .

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