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
The input into the function is t
The output of the function is b(t) Think of t as the xvalue {input} Think of b(t) as the yvalue {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.) Ask Algebra House
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