The number of degrees in dentistry (D.D.S. or D.M.D.) conferred to females in the United States has been increasing steadily in recent decades. Based on data from the National Center for Education Statistics, the rate of change of the number of bachelor’s degrees can be approximated by the function

where t is the number of years since 1980.

a. Find D(t), given that about 700 degrees in dentistry were conferred to females in 1980 (t = 0).

b. Use the formula from part a to project the number of degrees in dentistry that will be conferred to females in 2015 (t = 35).

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D'(t) = 29.25e0.035721