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Llana [10]
2 years ago
14

The graph shows the amount of a medicine min milligrams, remaining in a patient's body hours after receiving an injection . The

amount of the medicine decreases exponentially
a.By what factor did the medicine decrease in the hour and a half?

b. By what factor did the medicine decrease in the first half hour?


—What about in the first hour?

C. Write an equation relating m, the number of milligrams of the drug in the patient's body, and hthe number of hours since the injection
Mathematics
1 answer:
aksik [14]2 years ago
6 0

An exponential function is a function defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>(a) The factor at which the medicine decreased, in 1.5 hour</h3>

From the graph, we have the following ordered pairs

(x,y) = (0,270) and (1.5,80)

Given that:

y = ab^x

At point (0,270), we have:

ab^0=270

a= 270

At point (1.5,80), we have:

ab^{1.5} = 80

Substitute 270 for a

270b^{1.5} = 80

Divide both sides by 270

b^{1.5} = 0.2963

Take 1.5th root of both sides

b =0.44

Hence, the medicine decrease in the hour and half at a factor of 0.44

<h3>(b) The factor at which the medicine decreased in the first half hour, and the first hour</h3>

In (a), we have:

The decay factor (b) to be 0.44

This represents the factor at which the medicine decreased throughout.

Hence, the medicine decrease in the first half hour, and the first hour at a factor of 0.44

<h3>(c) The exponential equation</h3>

In (a), we have:

a= 270

b = 0.44

So, the exponential equation is:

y =270 * 0.44^x

In terms of m and h, we have:

m =270 * 0.44^h

Hence, the equation relating m to h is m =270 * 0.44^h

Read more about exponential equations at:

brainly.com/question/11832081

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