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

A.) 24.0 E.) bacteria

B.) 24.8 F.) minutes

C.) 25.4 G.) bacteria per minute

D.) 25.6 H.) minutes per bacteria

**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 x-value {input}

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

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}

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}

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

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 coordinatesIf 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 coordinatesy2 - 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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