A growth relationship is y 10ee t At what time t does y equ

A growth relationship is: y = 10e^e^ t. At what time, t, does y equal 100? 3.070 0.531 5.261 0.726 1.151

Solution

We have y = 10e^2t . When y = 100, we have 100 = 10e^2t . or, e^2t = 10. On taking natural logarithms of both the sides, we have 2t lne = ln10 or, 2t = ln 10 ( as ln e = 1). Thus 2t = 2.302585093. Therefore, t = 1/2(2.302585093.) = 1.151292547 or, t = 1.151 (on rounding off to 3 decimal places) The answer is (e).