Question

after a certain medicine is injected, its concentration in the bloodstream changes exponentially over time.
the graph describes the medicines concentration (in milligrams per liter) over time (in hours).
how does the medicines concentration change over time?
choose 1 answer:
a the medicines concentration drops by 30% each hour.
b the medicines concentration increases by 30% each hour.
c the medicines concentration drops by 70% each hour.
d the medicines concentration increases by 70% each hour.

Explanation:

Step1: Identify initial concentration

At $t=0$, concentration $C_0=100$ mg/l.

Step2: Check concentration at t=1

At $t=1$, concentration $C_1=70$ mg/l.

Step3: Calculate change percentage

Find the percentage change:
$$\text{Change} = \frac{C_1 - C_0}{C_0} \times 100\% = \frac{70-100}{100} \times 100\% = -30\%$$
The negative sign means a drop of 30%.

Step4: Verify with t=2

At $t=2$, $C_2=49$ mg/l.
$$\text{Change from } t=1: \frac{49-70}{70} \times 100\% = -30\%$$
Confirms consistent 30% hourly drop.

Answer:

A. The medicine's concentration drops by 30% each hour.