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
[tex]\begin{gathered} M\text{ = 65,536 }\times\text{ 4}^h \\ \text{where h represents the number of hours after 8:00am} \end{gathered}[/tex]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:
[tex]\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}[/tex]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
