the temperature of a certain cup of coffee 5 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
"first , we have to find a . we know that after t = 5 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 5 a ) + 60 60 = 120 * ( 2 ^ - 5 a ) 60 / 120 = 2 ^ - 5 a 1 / 2 = 2 ^ - 5 a 2 ^ - 1 = 2 ^ - 5 a - 1 = - 5 a 1 / 5 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 5 * 30 ) + 60 f = 120 * ( 2 ^ - 6 ) + 60 f = 120 * ( 1 / 2 ^ 6 ) + 60 f = 120 * 1 / 64 + 60 f = 1.875 + 60 = 61.875 answer b !"
add(multiply(power(2, multiply(divide(60, 5), subtract(const_1, 2))), 120), 60)