Question

All exponential functions can be written in many forms. Write the function

f(t) = 2800(0.95)' in the form f(t) = abro. Round all coefficients to four
decimal places.

Answer 1

`2800(0.95)^t~~ = ~~2800(b)^{(t)/(10)}\implies \cfrac{2800(0.95)^t}{2800}=b^{(t)/(10)}\implies 0.95^t=b^{(t)/(10)} \\\\\\ (0.95)^{(10t)/(10)}=b^{(t)/(10)}\implies (0.95^(10))^{(t)/(10)}=b^{(t)/(10)}\implies (0.5987)^{(t)/(10)}\approx b^{(t)/(10)}\implies 0.5987 \approx b \\\\[-0.35em] ~\dotfill\\\\ ~\hfill f(t)\approx 2800(0.5987)^{(t)/(10)}~\hfill`