Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 2^−x and y = 4^x + 3 intersect are the solutions of the equation 2^−x = 4^x + 3.

Part B: Make tables to find the solution to 2^−x = 4^x + 3. Take the integer values of x only between −3 and 3.

Part C: How can you solve the equation 2^−x = 4^x + 3 graphically?

207/8 is the right

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies