1. The polynomial function, w = 0.0071d3 – 0.09d2 + 0.48d, models the weight of the ideal round-cut diamond where w is the diamond’s weight (in carats) and d is the diameter (in millimeters). Based on the model, find the weight of the diamond with a diameter of 20 millimeters. 2. A drugstore that sells a certain brand of Vitamin C tablets predicts that their profit P can be modeled by the polynomial function P(a) = -50a3 + 2400a2–2000, where a is the amount spent on advertising (in thousands of pesos). What is its profit if a = 16? 3. Suppose that the total number attendance A (in thousands) at NCAA women’s basketball games is modeled by the polynomial function A = -1.95t3 + 70.1t2 – 188t + 2150, from 2000 to 2018, where t is the number of years since 2000. Find the attendance for the year 2009. 4. The number of eggs, E(x), in a female butterfly is a function of her abdominal width, x, in millimeters, modeled by E(x) = 14x3 – 17x2 – 16x + 34. How many eggs can the butterfly carry if the width of her abdomen is 4 millimeters? 5. A pyramid can be formed using same sized balls. For example, 3 balls can be arranged in a triangle, then the fourth ball placed in the middle on top of them. The total number of balls used can be modeled by the polynomial function, P(n)= 1/6n(n+1)(n+2) , where n is the number of balls on each side of the bottom layer. What is the total number of balls used to form a pyramid if there are 5 balls on each side of the bottom layer?
Direction: Answer the following question through evaluating each given polynomial
function.
Kindly answer all the questions please. With solution. Thank you in advance.
1. The polynomial function, w = 0.0071d3 – 0.09d2 + 0.48d, models the weight of
the ideal round-cut diamond where w is the diamond’s weight (in carats) and d
is the diameter (in millimeters). Based on the model, find the weight of the
diamond with a diameter of 20 millimeters.
2. A drugstore that sells a certain brand of Vitamin C tablets predicts that their
profit P can be modeled by the polynomial function P(a) = -50a3 + 2400a2–2000, where a is the amount spent on advertising (in thousands of pesos).
What is its profit if a = 16?
3. Suppose that the total number attendance A (in thousands) at NCAA women’s
basketball games is modeled by the polynomial function
A = -1.95t3 + 70.1t2 – 188t + 2150, from 2000 to 2018, where t is the number of
years since 2000. Find the attendance for the year 2009.
4. The number of eggs, E(x), in a female butterfly is a function of her abdominal
width, x, in millimeters, modeled by E(x) = 14x3 – 17x2 – 16x + 34. How many
eggs can the butterfly carry if the width of her abdomen is 4 millimeters?
5. A pyramid can be formed using same sized balls. For example, 3 balls can be
arranged in a triangle, then the fourth ball placed in the middle on top of them.
The total number of balls used can be modeled by the polynomial function, P(n)= 1/6n(n+1)(n+2)
, where n is the number of balls on each side of the
bottom layer. What is the total number of balls used to form a pyramid if there
are 5 balls on each side of the bottom layer?
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