\fA certain population is modeled by the differentiable function P, where P(t) is the population in thousands and t is the time in years. The function P satisfies the logistic differential equation ap at = 0.04 P(20 - P), and P(1) = 10. What is the value of P (1) A -0.64 B -0.04 D 1.2The series 1 + 2x + 3x + 4x + ... + nx-+ ... is the Maclaurin series for which of the following functions? A (1-x)2 B 1 (1+x)2 C 1 1-2x D X 1 - x +1The Taylor series for a function f about x = 0 is given by T(x) =2+3x-4x 1x2 _ 1x3 - 1x4+ 4x + 3x+ ... and converges to f(x) for all real numbers. Let P4(x) be the fourth-degree Taylor polynomial for f about x = 0. Which of the following inequalities guarantees that f ( ) - PA (} ) S k ? $ ( 2)