12. A population of wolves in af country is represented by the equation \( P(t)=80(0.98)^{\prime} \), where \( t \) is the number of years since 1998 . What will be the number of wolves in the population in the year 2012 ? B. 52 B. 56 D. 60

To find the number of wolves in the population in the year 2012, we need to substitute the value of \( t \) into the equation \( P(t)=80(0.98)^{\prime} \) and calculate the result. Given: - The equation representing the population of wolves is \( P(t)=80(0.98)^{\prime} \). - The year 2012 is 14 years after 1998, so \( t = 14 \). Substitute \( t = 14 \) into the equation: \[ P(14) = 80(0.98)^{14} \] Now, we can calculate the number of wolves in the population in the year 2012. Calculate the value by following steps: - step0: Calculate: \(80\times 0.98^{14}\) - step1: Convert the expressions: \(80\left(\frac{49}{50}\right)^{14}\) - step2: Simplify: \(80\times \frac{49^{14}}{50^{14}}\) - step3: Rewrite the expression: \(10\times 8\times \frac{49^{14}}{50^{14}}\) - step4: Rewrite the expression: \(10\times 8\times \frac{49^{14}}{10^{14}\times 5^{14}}\) - step5: Reduce the numbers: \(8\times \frac{49^{14}}{10^{13}\times 5^{14}}\) - step6: Rewrite the expression: \(8\times \frac{49^{14}}{2^{13}\times 5^{13}\times 5^{14}}\) - step7: Rewrite the expression: \(2^{3}\times \frac{49^{14}}{2^{13}\times 5^{13}\times 5^{14}}\) - step8: Reduce the numbers: \(1\times \frac{49^{14}}{2^{10}\times 5^{13}\times 5^{14}}\) - step9: Multiply the fractions: \(\frac{49^{14}}{1024\times 5^{27}}\) The number of wolves in the population in the year 2012 will be approximately 60.29.