{1 point} The population of Peru (in millions of people) can be approximately modeled by the equation P(t) = 2813"-1t , where t is years since 2010. :1) Using derivatives, calculate how fast the population was growing in 2017. Growth rate: EEE million people per year b) In what year will the population be growing by 8, 000, 000 people per year? Year: 5E5 (1 point) Using the following table, evaluate the following quantities. 0 1 2 3 4 5 f(ac) 5 4 0 5 f' (x) 0 4 5 3 0 g(a) 1 3 5 5 0 g'(x 0 1 1 3 4 a) h'(2) where h(a) = f(ze)g(z) h'(2) = b) h'(4) where h(x) = f(x) + g(x) h'(4) = c) h'(1) where h(x) = f(x) f(x) h'(1) = d) h'(3) where h(x) = x2g(x) h'(3) = e) h'(5) where h(x) = g(x)(ex + 1) h'(5) = f) h'(2) where h(x) = f(x)g(a)x2 h'(2) = g) h'(5) where h(x) = f(x) f(x)g(z) h' (5) : h) h'(1) where h(x) = 49(x) h'(1) =(1 point) Let f(x) = x(2 + 3e] ) a) Find the equation of the tangent line to f at x = 0. Tangent line: y b) Find the equation of the tangent line to f at x = 3. Tangent line: y =(1 point) a) Find the quadratic polynomial g(a) = ax + ba + c which best fits the function f(ae) = ed at a = 0, in the sense that g(0) = f(0), g'(0) = f'(0), and g"(0) = f"(0). g(z) = b) Find the quadratic polynomial g(a) = ax + ba + c which best fits the function f(a) = 6ed at a = 0, in the sense that g(0) = f(0), g'(0) = f'(0), and g"(0) = f"(0). g(a) =(1 point) Certain baseball cards increased very rapidly in value over the past decade. For example, the price of a particular card was modeled by V(t) = 78(1.28) where V(t) is the price (in dollars) of the card t years after 2007. Find the rate, in dollars per year, at which the price is increasing at time t. Rate at time t: dollars per year