Question

A medicine loses 20% of its effectiveness each hour. If you start with 100mg, how much is effective after 4 hours?

a) Circle: growth or decay

b) Fill in the blanks from the problem above:



initial amount = _______



rate = ______



x = _____

c) Convert the rate from a percent to a decimal.



_____% = _______

Answer 1

a) This is an example of decay.

b) Fill in the blanks from the problem above:

initial amount = 100 mg

rate = 20%

x = 4 hours

c) Convert the rate from a percent to a decimal.

20% = 0.20

Now, to determine how much of the medicine is still effective after 4 hours, you can use the formula for exponential decay:

\[
A = A_0 \times (1 - r)^t
\]

Where:
- \(A_0\) is the initial amount (100 mg)
- \(r\) is the rate of decay (0.20)
- \(t\) is the time in hours (4)

Substituting the values into the formula gives:

\[
A = 100 \times (1 - 0.20)^4
\]

\[
A = 100 \times (0.80)^4
\]

Calculating \( (0.80)^4 \):

\[
(0.80)^4 = 0.4096
\]

Now substituting back into the equation:

\[
A = 100 \times 0.4096 = 40.96
\]

Thus, after 4 hours, approximately 40.96 mg of the medicine is still effective.