Having completed your first few tasks, you move now to a portion of the lab where important bacteria are being grown. Based on the data collected, you have determined that the population of this bacteria in the range measured can be modeled as \( A(t)=185(1.11)^{t} \), where \( t \) is given in days. To the nearest whole number, what will the bacteria population be after 6 days? The bacteria population will be Number Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using appropriate mathematical concepts to support your co-workers and supervisor.

To find the population of bacteria after 6 days, we can substitute \( t = 6 \) into the given model \( A(t) = 185(1.11)^t \) and calculate the result. Given model: \( A(t) = 185(1.11)^t \) Substitute \( t = 6 \) into the model: \( A(6) = 185(1.11)^6 \) Now, we can calculate the population of bacteria after 6 days by substituting \( t = 6 \) into the model and solving for \( A(6) \). Calculate the value by following steps: - step0: Calculate: \(185\times 1.11^{6}\) - step1: Convert the expressions: \(185\left(\frac{111}{100}\right)^{6}\) - step2: Simplify: \(185\times \frac{111^{6}}{100^{6}}\) - step3: Rewrite the expression: \(5\times 37\times \frac{111^{6}}{100^{6}}\) - step4: Rewrite the expression: \(5\times 37\times \frac{111^{6}}{25^{6}\times 4^{6}}\) - step5: Rewrite the expression: \(5\times 37\times \frac{111^{6}}{5^{12}\times 4^{6}}\) - step6: Reduce the numbers: \(37\times \frac{111^{6}}{5^{11}\times 4^{6}}\) - step7: Multiply the fractions: \(\frac{37\times 111^{6}}{4096\times 5^{11}}\) The population of bacteria after 6 days will be approximately 346.03. Therefore, after 6 days, the bacteria population will be approximately 346.