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AnnyKZ [126]
3 years ago
11

Soon after taking an aspirin, a patient has absorbed 320 mg of the drug. after 3 hours, only 40 mg remain. find an exponential m

odel for the amount of aspirin in the bloodstream after t hours
Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0
The equation will be of the form:
A(t)= A_{0} e^{rt}
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
40=320e^{3r}
Rearranging and taking natural logs of both sides, we get:
ln\ 0.125=3r
r=\frac{ln\ 0.125}{3}=-0.693
The required model is:
A=A _{0} e^{-0.693t}
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Jobisdone [24]

The value of f[ -4 ] and g°f[-2] are \frac{14}{3} and 13 respectively.

<h3>What is the value of f[-4] and g°f[-2]?</h3>

Given the function;

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For f[ -4 ], we substitute -4 for every variable x in the function.

f(x) = \frac{3x-2}{x+1}\\\\f(-4) = \frac{3(-4)-2}{(-4)+1}\\\\f(-4) = \frac{-12-2}{-4+1}\\\\f(-4) = \frac{-14}{-3}\\\\f(-4) = \frac{14}{3}

For g°f[-2]

g°f[-2] is expressed as g(f(-2))

g(\frac{3x-2}{x+1}) =  (\frac{3x-2}{x+1}) + 5\\\\g(\frac{3x-2}{x+1}) =  \frac{3x-2}{x+1} + \frac{5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) =  \frac{3x-2+5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) =  \frac{8x+3}{x+1}\\\\We\ substitute \ in \ [-2] \\\\g(\frac{3x-2}{x+1}) =  \frac{8(-2)+3}{(-2)+1}\\\\g(\frac{3x-2}{x+1}) =  \frac{-16+3}{-2+1}\\\\g(\frac{3x-2}{x+1}) =  \frac{-13}{-1}\\\\g(\frac{3x-2}{x+1}) =  13

Therefore, the value of f[ -4 ] and g°f[-2] are \frac{14}{3} and 13 respectively.

Learn more about composite functions here: brainly.com/question/20379727

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