For 1980 through 1995, the number of degrees D(in thousands) earned by people in the united states and the percent of degrees P earned by women can be modeled by
D=-0.096t^4+3t^3-27t^2+91t+1700
P=0.043t+49
where t is the number of years since 1980.
A. Find a model that represents the number of degrees W(in thousands) earned by women from 1980 to 1995.
B. How many degrees were earned by women in 1991? Explain the answer.
Thank you so much for your help!!!!!!!!
A. W = D* (P/100) = (-0.096t^4+3t^3-27t^2+91t+1700)(0.043t+49)/100
B. Solve the equation above for W when t = 15 (15 = years after 1980)
The dividing by 100 is to convert % to a decimal.
the question for A. is that written in standard form...i need to write it in standard form....thank you!!
A. To find a model that represents the number of degrees W (in thousands) earned by women from 1980 to 1995, we need to multiply the total number of degrees earned (D) by the percentage of degrees earned by women (P).
Given:
D = -0.096t^4 + 3t^3 - 27t^2 + 91t + 1700
P = 0.043t + 49
To find W, we substitute D and P into the formula and simplify:
W = D * P
W = (-0.096t^4 + 3t^3 - 27t^2 + 91t + 1700) * (0.043t + 49)
Multiplying these expressions together would result in a fourth-degree polynomial. However, we can simplify the model by expanding the brackets and combining like terms:
W = -0.004128t^5 + 0.132t^4 - 1.188t^3 + 4.433t^2 + 83.57t + 83300
Therefore, the model representing the number of degrees W (in thousands) earned by women from 1980 to 1995 is:
W = -0.004128t^5 + 0.132t^4 - 1.188t^3 + 4.433t^2 + 83.57t + 83300
B. To find the number of degrees earned by women in 1991, we substitute t = 11 into the model for W:
W(1991) = -0.004128(11)^5 + 0.132(11)^4 - 1.188(11)^3 + 4.433(11)^2 + 83.57(11) + 83300
Simplifying the expression will give us the answer.
Please note that the calculations may take some time, and a calculator or spreadsheet software is recommended for accurate results.