Step 1 :Given that the number of cells in a tumor doubles every 4.5 months, we can model this as an exponential growth problem. The formula for exponential growth is \(A = P * (1 + r/n)^{nt}\), where:
Step 2 :\(A\) is the final amount of cells after \(n\) years.
Step 3 :\(P\) is the initial amount of cells (in this case, 1).
Step 4 :\(r\) is the growth rate (in this case, 100% or 1 in decimal form).
Step 5 :\(n\) is the number of times the cells double per year (in this case, 12/4.5 = 2.67 times).
Step 6 :\(t\) is the time the cells are growing for in years (in this case, 2 years).
Step 7 :Substituting these values into the formula, we get \(A = 1 * (1 + 1/2.67)^{2.67*2}\).
Step 8 :Calculating this gives \(A = 5.465304833469831\).
Step 9 :Rounding this to the nearest whole number, we get \(A = 5\).
Step 10 :Final Answer: There will be \(\boxed{5}\) cells after 2 years.