The graph of a function f is shown below Use this graph to d

The graph of a function f is shown below. Use this graph to determine the average rate of change for f as the input values change from x = -5 to x = 4. (a) Average rate of change is 3 (b) Average rate of change is 0 (c) Average rate of change is 5/4 (d) Average rate of change is 1/3 (e) Average rate of change is 1/2. The purchasing power of one dollar at a point in time is the amount of money needed today to purchase the item. Let P represent the purchasing power of one dollar t years from 2015, and suppose P = f(t) = 0.97^t. Approximately how many years from 2015 will it take for the purchasing power of the dollar to reach 79 cents? (a) Approximately 7.74 years (b) Approximately 27.24 years (c) Approximately 0.81 year (d) Approximately 0.08 years (e) Approximately 5.25 years Darren notices that his son has let the bathroom sink fill with water. Darren pulls the plug, and the sink drains at the constant rate of 22 mL every three woods. Let V represent the volume of water (measured in mL) in the sink, and let t represent the number of seconds since Darren pulled the plug. When the value of t increases from 8 seconds to 20 seconds, what is the corresponding change in the value of V? (a) Delta V = 12 mL (b) Delta V = -12 mL (c) Delta V = -88 mL (d) Delta V = 264 mL (e) Delta V = 88 mL A bag of grocerics is sitting on your kitchen table. Which of the following is a quantity? I The bag II The volume of the bag in cubic inches III The groceries in the bag IV The temperature in degrees Celsuis of the egg carton at the bottom of the bag (a) only I and III (b) Only II and IV (c) Only I and II (d) Only III and IV (e) All are quantities.

Solution

30) at x =-5 value of f =-6

at x =4 value of f =-3

average rate of change =(-3-(-6))_/(4-(-5))

average rate of change =(-3+6)_/(4+5)

average rate of change =3_/9

average rate of change =1_/3

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31)

given P=f(t)=0.97^t

purchasing power of dollar to reach 79 cents =0.79 dollars

0.97^t=0.79

t=ln_0.970.79

t=(ln0.79)/(ln0.97)

t =7.73895

approximately 7.74 years