The number of degrees in dentistry conferred to females in the united states has

Question

The number of degrees in dentistry 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 the number of dentistry degrees can be approximated by the function

D'(t)= 35.352e0.017676t, where t is the number of years since 1980.

(a) find D(t), given that 1695 degrees in denstistry were conferred to females in 2001.

(b) use the formula from part (a) to project the number of degrees in dentistry that will be conferred to females in 2020.

Please show all steps.

Explanation / Answer

a> D'(t)= 35.352e0.017676t

To find D(t) we'll integrate the above function with respect to time 't' in years

D'(t) = dD(t)//dt = 35.352e^(0.017676t)

dD(t) = 35.352e^(0.017676t)dt

integrating both sides

=> D(t) = 35.352e^(0.017676t)/0.017676 + C , -----> C is the integration constant

now the initil conitions are :

t = 0 at 1980 and t = 21 at 2001

and D(21) = 1695

=> 1695 = 35.352e^(0.017676*(21))/0.017676 + C

=> C = -1209.93

=> the required function is :

D(t) = 35.352e^(0.017676t)/0.017676 - 1209.93

b> from 1980 to 2020 ,t = 40 years

=> D(40) = 35.352e^(0.017676*40)/0.017676 - 1209.93

D(40) = 2846.03 = 2846 degrees

Hence in 2020 2846 degrees would be conferred to females

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