Fat travels through the bloodstream attached to protein in a combination called a lipoprotein. Low-density lipoprotein (LDL) picks up cholesterol from the liver and delivers it to the cells, dropping off any excess cholesterol on the artery walls. Too much LDL in the bloodstream increases the risk of heart disease and stroke. A patient with a high level of LDL receives a drug that is found to reduce the level at a rate given by L'(t) = −0.3t(49 − t²)^0.4 units/day where t is the number of days after the drug is administered, for 0 ≤ t ≤ 7.

a. By how much does the patient’s LDL level change during the first 3 days after the drug is administered?

b. Suppose the patient’s LDL level is 120 at the time the drug is administered. Find L(t).

c. The recommended “safe” LDL level is 100. How many days does it take for the patient’s LDL level to be “safe”?