The function that represents the amount of caffeine in milligrams remaining

Mathematics

2 answers:

RUDIKE [14]4 years ago

7 0

Answer:

If you are referring to a logarithmic function with a continuous rate of decrease(as implied by remaining), then here is your answer:

A(t) = c×e^(dt)

where c is the starting amount of caffeine in miligrams, e is euler's number (base of a natural logarithm), and d is continuous rate of logarithmic change(as a percentage decay(negative)) per t(time) in standard unit of time(i.e hours)

I.e(for instance): if you are given a cup of coffee with an initial 190 mg of caffeine, leaving the body at a rate of 36% every hour.

This relationship solving for the remaining miligrams can be given by:

A(t) = 190 mg × e ^ (-.36t)

Where t is the amount of hours.

fredd [130]4 years ago

4 0

Answer:

Step-by-step explanation:

The function that represents the amount of caffeine, in milligrams, remaining in a body after drinking two mountain dew sodas is given by f(t) = 110(0.8855)^t, where t is time in hours.

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3 less than the quotient of 20 and x

UkoKoshka [18]

It would be (20/x) -3

3 0

3 years ago

HELP ME WITH MATHHHHH ILL GIVE YOU BRAINLIEST

Alla [95]

Answer:

-3, 1, 4 are the x-intercepts

Step-by-step explanation:

The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).

In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.

For the given polynomial, we notice that the sum of the coefficients is zero:

1 -2 -11 +12 = 0

This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.

Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...

f(x) = (x -1)(x² -x -12)

We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...

f(x) = (x -1)(x -4)(x +3)

Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.

The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.