Question

If a patient doesn't receive treatment

for a certain injury within 2 hours after
injury, the patient's chance of survival
starts decreasing by 15% each hour. If
no treatment has been given within 4
hours after injury, roughly, what chance
of survival will the patient have?

Answer 1

Explanation:

calculate the chance of survival step by step:

The patient's chance of survival decreases by 15% each hour without treatment.

After 2 hours without treatment, the chance of survival is decreased by 15% twice (15% x 2).

After 4 hours without treatment, the chance of survival is decreased by 15% four times (15% x 4).

Let's denote the initial chance of survival as

P. After 2 hours without treatment, the chance of survival is

−

0.15

−

0.15

=

0.7

P−0.15P−0.15P=0.7P. After 4 hours without treatment, the chance of survival is

0.7

−

0.15

−

0.15

−

0.15

−

0.15

=

0.25

0.7P−0.15P−0.15P−0.15P−0.15P=0.25P.

So, roughly, if no treatment has been given within 4 hours after the injury, the patient's chance of survival will be about 25%.