Math 1P97. Assignment 5 (4%). Due date: Monday, June 27, 6:45pm Student's name: Total mark: NOTE: Students are expected to complete ALL questions on the assignment. However, only a subset of questions will be considered for marking. Marks will be deducted for incomplete assignments. Show all your work. 1. Find the indefinite integrals. Z a) Z b) Z c) 3 8 4x + 2 dx = e3x+5 dx = 8 dx = x2 8x + 16 Z d) Z e) 2x dx = 8 x2 + 3 6xe3x 2 +5 dx = Z p 3 ln(x + 3) dx f) = x+3 Z g) (3x2 + 8x 16) dx = 5 x3 + 4x2 16x + 64 2. (Heights of children, pr. 89) According to the Jenss model for predicting the height of preschool children, the rate of growth of a typical preschool child is \u0012 \u0013 1 t R(t) = 26e + 6.4 t6 4 centimeters per year, where t is measured in years. The height of a typical 3-month-old preschool child is 60 cm. a) Find a model for predicting the height of a typical preschool child at age t. b) Estimate the height of a typical 3-yr-old child. 3. Evaluate the definite integral. Z1 a) (x3 9x2 + 3 x + 28) dx = 0 Z1 b) 1 (x2 2x + 1)2 dx = Z4 c) x x2 + 9 dx = 0 Z1 d) e x dx = x 0 Ze e) ln3 x dx = x 1 Z1 f) 2 4x3 3x2 + 1 dx = x2 4. (Risk of Down syndrome, pr. 82) The rate at which the risk of Down syndrome is changing is approximated by the function r(x) = 0.004641x2 0.3012x + 4.9 (20 x 45) where r(x) is measured in percentage of all births/year and x is the maternal age at delivery. a) Find a function f giving the risk as a percentage of all births when the maternal age at delivery is x years, given that the risk of Down syndrome at age 30 is 0.14% of all births. b) Based on this model, what is the risk of Down syndrome when the maternal age at delivery is 25 years? c) What is the risk of Down syndrome when the maternal age at delivery is 45 years? 5. Find the area of the region enclosed by the following graphs. a) y = x2 4x 8, y = x2 + 8 b) xy = 6, x+y =7 c) y 2 = 3x, x2 = 3y 6. (International air traffic, pr. 65) International air traffic in and out of the United States is projected to grow at the rate of R(t) = 6.7e0.05t (2 t 20) million passengers per year between 2012 and 2030. Here, t = 2 corresponds to 2012. The number of passengers in 2012 was 160 million. a) Find the expression for the projected number of passengers in year t. b) What is the projected number of passengers in 2016? c) What is the estimated average growth rate of international air traffic in and out of the United States from 2012 to 2030? Zb Hint: The average value (AV) of f over [a, b] is AV = 1 f (x) dx ba a