A medical researcher is investigating a new kind of bacterial infection. In her lab, she is studying the bacteria that cause the infection. After the first hour, there were 4 bacteria. After the second hour, she discovers that the amount of bacteria quadrupled. If the bacteria continue to quadruple every hour, how many times more bacteria will there be after hour 4 than hour 1?
Start by filling in the rest of the table. Solve on paper if you need to. Then, enter your answers on Zearn.
Expanded Exponent Value
Hour 1 4 4
1
4
Hour 2 4·4 4
2
Hour 3 4·4·4 4
64
Hour 4 4·4·4·
4
4
256
Excellent!
How many more factors of 4 are in 4
4
than 4
1
?
Expanded Exponent Value
Hour 1 4 4
1
4
Hour 2 4·4 4
2
16
Hour 3 4·4·4 4
3
64
Hour 4 4·4·4·4 4
4
256
There are
more factors of 4 in 4
4
than 4
1
.
Good work!
Now, compare the number of bacteria after hour 4 to the number of bacteria after hour 1 using an exponent. There will be 4
4
bacteria after hour 4, and 4
1
bacteria after hour 1. How many times as many bacteria will there be after hour 4 than after hour 1?
Expanded Exponent Value
Hour 1 4 4
1
4
Hour 2 4·4 4
2
16
Hour 3 4·4·4 4
3
64
Hour 4 4·4·4·4 4
4
256
There are 3 more factors of 4 in 4
4
than 4
1
.
There will be 4
times as many bacteria after hour 4 than after hour 1.
Excellent!
Finally, compare the number of bacteria after hour 4 to the number of bacteria after hour 1 using an integer.
Expanded Exponent Value
Hour 1 4 4
1
4
Hour 2 4·4 4
2
16
Hour 3 4·4·4 4
3
64
Hour 4 4·4·4·4 4
4
256
There will be 43 times as many bacteria after hour 4 than after hour 1.
There will be
times as many bacteria after hour 4 than after hour 1.
