\[ P(t)=25(2)^{\frac{t}{1.06}} \] The number of yeast cells, $P(t)$, in a culture after $t$ days is modeled by the equation shown. After how many days will the population double in size? (Round your answer to the nearest hundredth.)

Step 1 ：The number of yeast cells, \(P(t)\), in a culture after \(t\) days is modeled by the equation \(P(t)=25(2)^{\frac{t}{1.06}}\). We want to find out after how many days will the population double in size.

Step 2 ：The population doubles when \(P(t) = 2P(0)\). We know that \(P(0) = 25\), so we need to solve the equation \(25(2)^{\frac{t}{1.06}} = 2*25\) for \(t\).

Step 3 ：We can simplify this equation to \(2^{\frac{t}{1.06}} = 2\), which implies that \(\frac{t}{1.06} = 1\). Solving for \(t\) will give us the number of days it takes for the population to double.

Step 4 ：\(t = 1.06\)

Step 5 ：Final Answer: \(\boxed{1.06}\)