A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 340. (a) Find an expression for the number of bacteria after 1' hours. P0?) = | x (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = bacteria (c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) t= 2.6 x hr Suppose that f(5) = 1, f '(5) = 7, g(5) = -9, and g'(5) = 5. Find the following values. (a) (fg)'(5) -58 (b) (f/g)'(5) 7/5 X (c) (g/f)'(5) 5/7 XIf f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). g 0 (a) Find u'(1). (b) Find v'(5).Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square increasing when the area of the square is 64 cm-? 48 X cm /s :Enhanced Feedback :Please try again, keeping in mind that the area of square of side a is a x a (A = a2). Differentiate this equation with respect to time t using the Chain Rule to find the equation the rate at which the area is increasing, dt ' UP. Then use the values from the exercise to evaluate the rate of change of the area of the square, paying close attention to the signs the rates of change of the side (positive when increasing and negative when decreasing). L - - - -If a snowball melts so that its surface area decreases at a rate of 9 cm/min, find the rate at which the diameter decreases when the diameter is 12 cm. -0.375 X cm/min :Enhanced Feedback Please try again. Keep in mind that the surface area of a snowball (sphere) with radius r is A = 4x2. Differentiate this equation with respect to time, t, using the Chain Rule, dt find the equation for the rate at which the area is decreasing, -. Then, use the values from the exercise to evaluate the rate of change of the radius of the sphere. Have in mi that the diameter is twice the radius