Question

The number of bacteria in a culture quadruples every hour. There were 65, 536 bacteria in the culture at 8:00 am. The expression 65,536 * 4^h models the number of bacteria in the culture h hours after 8:00 am.What is the value of the expression for h = -4?

Answer 1

the value of the expression for h = -4 is 256 bacterias

The number of bacteria multiplies by 4 every hour

Initial number of bacteria at 8.00am = 65,536

Let the model of the bacterial = M

`\begin{gathered} M\text{ = 65,536 }*\text{ 4}^h \\ \text{where h represents the number of hours after 8:00am} \end{gathered}`

When h = -4

Due to the negative, it means the number of bacterias decreases in 4 folds in each of the hours. So instead of multiplication by 4, we would be dividing by 4 in each of the hours.

M becomes:

`\begin{gathered} At\text{ h = 0 (at 8:00am) , M = 65,536} \\ \text{when h = -1 (at 7:00am)} \\ M\text{ = 65536/4 = 16384} \\ \text{when h = }-2 \\ M\text{ = 16384/4 = 4096} \\ \text{when h = -3} \\ M\text{ = 4096/4 = 1024} \\ \text{when h = -4 ( at 4:00am)} \\ M\text{ = 1024/4 = 256 bacterias} \end{gathered}`

Using the correct equation: 65536 * 4^h

At h = -4

M becomes = 65536/4^h due to the negative sign. h = 4

M = 65536/4^4 = 65536/256

M = 256 bacterias

Hence, the value of the expression for h = -4 is 256