Gestational diabetes mellitus $($GDM$)$ causes high blood sugar that can affect pregnancy and the baby's health. Oral glucose tolerance tests $($OGTT$)$ are used to measure how well the body can process a larger amount of sugar. The area under the curve $($AUC$)$ of the test is considered a measure of high blood sugar $($hyperglycemia$)$ in pregnant women. Those with an AUC higher than $305mg*\frac{h}{d}L$ should undergo aggressive management due to a higher risk of adverse pregnancy outcomes.

Determine the AUC for the data in the following figure and conclude whether the pregnant woman should undergo aggressive management or not. Initially, the blood glucose level is $98\mathrm{.}03m\frac{g}{d}L.$ Use four $(4)$ decimal places for each step of your calculation.