QUESTION 1

a. Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and let the Area of the region enclossed by the rectangle be A ( square units). Express A as a function of w and state the domain and range of the function. AP (4 each)

b. The population P of a certain small-town t years from now is predicted to be p(t)=35000+10000/(t+2)³ . In your own method estimate the population of the town in the long run. AN (6)

M a. Let f {x} = stn(ax + in} and let 3 (x) = cos(cx + b} where a and b are constants. Gues a formular for #0:) and g\"(x] for general It {positive integer ) av {31 h} Use the method of Differentiation from rst principle to prove that the derivative of the square root of x is given below. (1 l -I= d1 2,1; CR (3} i. Your friend claims you can use the change of base to write the expression (In I} as a common logarithm. Is your friend correct? Explain your reasoning. i. There is a Covid 19 Pandemic in the world. This appeared in Ghana and affected 5 people. |[Zorvid 19 affects 2 people a day. How long does it take for there to be 1,000,000 covid 19 affected people in Ghana also how many.r covid 19 people will there he on day 8 '