Assuming that the f−18 can be transported at 59.0 miles/hour, how close must the hospital be to the cyclotron if 68% of the f−18 produced is to make it to the hospital?

60.12 miles

Explanation:

Using the calculation formula shown below:

\frac{N_{o} }{N_{t} } }" alt="log_{2}" />\frac{N_{o} }{N_{t} } }" />

where:

is the half life, is the original amount of F-18, and is the remaining amount of F-18 at time t.

Generally, F-18 has an half life of 1.83 hours.

Therefore:

\frac{100}{68} = 1.02 hours" alt="log_{2}" />\frac{100}{68} = 1.02 hours" />

Therefore using a speed of 59 miles/hour, the closeness of the hospital is:

distance = speed*time = 59*1.02 = 60.12 miles