The dollar value of two Investments after t years is given b

The dollar value of two Investments after t years is given by f(t)= 1000(1.15)^t and g(t) = 800(1.79)^t. After how many years are the two investments worth the exact same amount? t = __________________

Solution

f(t)= 1000(1.15)^t   and g(t)= 800(1.79)^t are the values of two investments made for a certain number of years \'t\'.

Since, f(t) = g(t) , we have :   1000(1.15)^t = 800(1.79)^t

1000/800 = (1.79/1.15)^t

1.25 = 1.55^t

Taking log on both sides we get : log 1.25 = t* log 1.55

or t = log 1.25/ log 1.55 = 0.5 years or 6 months.....(Answer)