I have an original exponential function:
$1000 \cdot 2^{0.1x}$
At the point $\big( 18+6 \frac {\log5} {\log2} (\approx 31.93) , 9146 \big)$, I'm looking to know if it is possible to derive an exponential function which continues on from the original exponential function, from only the following information:
- At $18+6 \frac {\log5} {\log2}$, the rate of change of the new exponential function is: $(2^{0.1})^{\big(18+6 \frac {\log5} {\log2}\big)} \cdot \ln(2^{0.1}) \approx 633.959$.
(This is actually the intercept point between $x=18+6 \frac {\log5} {\log2}$ and the $\frac {\Bbb d} {\Bbb dx} (1000 \cdot 2^{0.1x})$.)
- The new function plateaus by $28+6 \frac {\log5} {\log2}$ (i.e., reaches its horizontal asymptote $-1$ by $x=28+6 \frac {\log5} {\log2}$).
