Question

willa is studying the growth rate of a specific type of organism called a ciliate. she places 5 cells in a dish and records the number of cells over time. the table shows her results. if the pattern continues, how many cells will be in the dish after 8 hours? express your answer as a power. _ cells

Explanation:

Step1: Analyze the pattern

At \(0\) hours: \(5 = 5^1\)
At \(2\) hours: \(5\times5=5^2\)
At \(4\) hours: \(5\times5\times5 = 5^3\)
We can see that the exponent of \(5\) is \(\frac{\text{number of hours}}{2}+ 1\)

Step2: Calculate for 8 hours

For \(t = 8\) hours, the exponent \(n=\frac{8}{2}+1=5\)

Answer:

\(5^5\) cells