For each scenario below, find the matching growth or decay model, f(t). v The concentration of pollutants in a lake is initially 100 ppm. The concentration A. L decays by 30% every 3 years. f(t) = 100 0.3 3 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' f0) = 100(1052'] 3 hours. 100 bacteria begin a colony in a petri dish. The bacteria increase by 200% every 0.1:\") = 1008\"] half hour. The cost of producing high end shoes is currently $100. The cost is increasing D. L by 50% every two years. f0) = 100 O 7 3 $100 million dollars is invested in a compound interest account. The interest rate is 5%, compounded every half a year. EIf(t)=100[1.5?t] E f0) = 100[1.33i] Math 0132 Tutorial 8 Worksheet: Finding Exponential Models 1. Vehicle Depreciation: Solve an Exponential Decay Problem A pickup truck sold for $50000 in 2010. Its book value, 10 years later, is $2815. a) Find an exponential decay model for the value of the vehicle, A(t), in $ as a function of time, t, in years from 2010, Mt) = A0 (in where T=1 year and the base, I), is related to the rate of depreciation per year. You will need a calculator. b) State the percentage the vehicle has depreciated each year, according to this model. c) According to this model, how many years would have to elapse in order for the vehicle value to reduce by half? Find an exact answer using a logarithm with base \"12" and then use the base change formula to convert this answer to base e. Use a calculator to get an answer to the nearest year