Question

HELP!!
The penicillin concentration, in micrograms per milliliter, in the
patient's bloodstream t minutes after the penicillin injection is
t
modeled by the function P defined by P(t) = 20065 . If P
approximates the values in the table to within 10 micrograms per
milliliter, what is the value of b, rounded to the nearest tenth?

Answer 1

They are inverse of logarithmic equations. The value of b to the nearest tenth is 0.1

Exponential equations

They are inverse of logarithmic equations. Given the exponential function that modelled the penicillin concentration, in micrograms per milliliter as shown:

$P(t) = 200b^{\frac{6}{5} }$

If the value of P(t) is 10, hence;

$10 = 200b^{\frac{6}{5} }\\\frac{10}{200} = b^{\frac{6}{5} } \\0.05= b^{\frac{6}{5} }$

Take the ln of both sides

ln0.05 = 6/5 lnb

-2.995 = 1.2 ln b

lnb = -2.495

b = e^-2.495

b = 0.08

Hence the value of b to the nearest tenth is 0.1

Learn more on exponential function here; https://brainly.com/question/2456547

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