How to map interval $[0, 100]$ to the interval $[100, 350]$? I have an interval $[0; 100]$ and would like to map it to this new interval: $[100;350]$.
I thought about multiplying it by $3.5$, but that would give the interval $[0;350]$. And adding to each of these elements $100$ would give: $[100;450]$. Hence my question: is it possible to do what I want?
Note that I can settle for the interval $[0;350]$ : in my program, it will be enough if I exclude the numbers present in the interval $[0;99]$.

Since $100\cdot t^0=100$ for any positive $t$, we find $t$ such that $100\cdot t^{100}=350\implies t=3.5^{0.01}$. $$\boxed{y=100\cdot3.5^{0.01x}}$$ In general an exponential mapping from $[a,b]$ to $[c,d]$ is $y=c\left(\frac dc\right)^{\frac{x-a}{b-a}}$.
