Interpret the average rate of change of a function

At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0.  The number of bacteria in the colony t minutes after the initial count is modeled by the function b(t) = 4(2)^t.  Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment?   Select all that apply.
A.)  24.0                      E.)  bacteria
B.)  24.8                      F.)  minutes
C.)  25.4                      G.)  bacteria per minute
D.)  25.6                      H.)  minutes per bacteria

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The input into the function is t
The output of the function is b(t)

Think of t as the x-value {input}
Think of b(t) as the y-value {output}

Rate of change is slope.

If t = 0
b(t) = 4(2)^0   {substituted 1, in for t, into b(t) = 4(2)^t}
      = 4(1)   {evaluated exponent}
      = 4   {multiplied}

(0,4) is one set of coordinates


If t = 5
b(t) = 4(2)^5   {substituted 5, in for t, into b(t) = 4(2)^t}
       = 4(32)   {evaluated exponent}
       = 128   {multiplied}
(5,128) is another set of coordinates

y2 - y1
--------- = slope
x2 - x1

(0,4) and (5,128)   {the two points}

128 - 4
----------- = slope   {substituted coordinates into slope formula}
  5 - 0

124
----- = slope   {subtracted in numerator and denominator}
  5

Rate of change is  24.8 bacteria per minute

B.)  and  G.)

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