SOLUTION: Write the exponential function y=8(1.25)^t in the form y=ae^kt. Once you have rewritten the formula, give k accurate to at least four decimal places. k=_ If t is measured in y

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write the exponential function y=8(1.25)^t in the form y=ae^kt. Once you have rewritten the formula, give k accurate to at least four decimal places. k=_ If t is measured in y      Log On


   



Question 1103993: Write the exponential function y=8(1.25)^t in the form y=ae^kt.
Once you have rewritten the formula, give k accurate to at least four decimal places.
k=_
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing decay the negative rate is implied).
(b) The annual growth rate is _% per year (round to the nearest 0.01%).
(c) The continuous growth rate is _% per year (round to the nearest 0.01%.
I tried working it out and I figured out that they were growth. My numbers (0.0025,8.20, and 0.25 respectively) were off.

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
8%281.25%29%5Et=8%2Ae%5E%28kt%29
1.25%5Et=e%5E%28kt%29
t%28ln%281.25%29%29=kt%28ln%28e%29%29
ln%281.25%29=k
k=0.22314

y=8%2Ae%5E%280.22314t%29

NOT decay; but is for exponential growth. k%3E0.