1000 = 50e^(2.5t) divide both sides by 50 20 = e^(2.5t) To clear the e, take the LN(natural log) of both sides. ln 20 = lne^(2.5t) We know that lne = 1, so we use this rule and the power rule to bring the 2.5t out of the power and in front of the lne. ln20 = 2.5t * lne ln20 = 2.5t * 1 ln20 = 2.5t divide both sides by 2.5 t = 1.2 hours
CHECK y = 50e^(2.5*1.2) y = 50 * 20 y = 1000 CHECKS
The graph of g(x) = -x^2 is a reflection in the x-axis of the graph of f(x) = x^2. Both graphs have one x-intercept as both graphs have their vertices at the origin, (0,0).