The number of visitors at a county fair grows at an annual rate of about \( 1.3 \% \). This year, the number of visitors was 12,304 . About how many visitors are expected 6 years from now? "Use the formula below. Round to the nearest whole. \( f(x)=a(1+r)^{t} \) 13,295 25,616 \( 1,821,434 \) 17,654

To find the expected number of visitors 6 years from now, we can use the formula for exponential growth: \[ f(x) = a(1 + r)^t \] Given: - Annual growth rate \( r = 1.3\% = 0.013 \) - Initial number of visitors \( a = 12,304 \) - Time period \( t = 6 \) years Substitute the given values into the formula: \[ f(6) = 12,304(1 + 0.013)^6 \] Now, we can calculate the expected number of visitors 6 years from now using the formula. Calculate the value by following steps: - step0: Calculate: \(12304\left(1+0.013\right)^{6}\) - step1: Add the numbers: \(12304\times 1.013^{6}\) - step2: Convert the expressions: \(12304\left(\frac{1013}{1000}\right)^{6}\) - step3: Simplify: \(12304\times \frac{1013^{6}}{1000^{6}}\) - step4: Rewrite the expression: \(16\times 769\times \frac{1013^{6}}{1000^{6}}\) - step5: Rewrite the expression: \(16\times 769\times \frac{1013^{6}}{8^{6}\times 125^{6}}\) - step6: Rewrite the expression: \(2^{4}\times 769\times \frac{1013^{6}}{2^{18}\times 125^{6}}\) - step7: Reduce the numbers: \(769\times \frac{1013^{6}}{2^{14}\times 125^{6}}\) - step8: Multiply the fractions: \(\frac{769\times 1013^{6}}{16384\times 125^{6}}\) The expected number of visitors 6 years from now is approximately 13,295. Therefore, the correct answer is 13,295.