QuestionFor each scenario below, find the matching growth or decay model, $f(t)$. $\$ 100$ million dollars is invested in a compound interest account. The interest rate is 5\%, compounded every half a year. $\qquad$ The concentration of pollutants in a lake is initially 100 ppm. The concentration decays by $30 \%$ every 3 years. The concentration of pollutants in a lake is initially 100 ppm. The concentration decays by 70\% every 3 years. 100 bacteria begin a colony in a petri dish. The bacteria increase by $30 \%$ every 3 hours. 100 bacteria begin a colony in a petri dish. The bacteria increase by 200\% every half hour. $\square$ The cost of producing high end shoes is currently $\$ 100$. The cost is increasing by $50 \%$ every two years.
1. $f(t)=100\left(0.7^{\frac{t}{3}}\right)$
2. $f(t)=100\left(0.3^{\frac{t}{3}}\right)$
3. $f(t)=100\left(1.3^{\frac{t}{3}}\right)$
4. $f(t)=100\left(3^{2 t}\right)$
5. $f(t)=100\left(1.5^{\frac{t}{2}}\right)$
6. $f(t)=100\left(1.05^{2 t}\right)$