10 A scientist is researching the effects of caffeine. She models the mass of caffeine in the body using
$$m = m _ { 0 } \mathrm { e } ^ { - k t }$$
where \(m _ { 0 }\) milligrams is the initial mass of caffeine in the body and \(m\) milligrams is the mass of caffeine in the body after \(t\) hours.
On average, it takes 5.7 hours for the mass of caffeine in the body to halve.
One cup of strong coffee contains 200 mg of caffeine.
10
- The scientist drinks two strong cups of coffee at 8 am. Use the model to estimate the mass of caffeine in the scientist's body at midday.
10 - The scientist wants the mass of caffeine in her body to stay below 480 mg
| 10 |
| Use the model to find the earliest time |
| coffee. |
| Give your answer to the nearest minute |