Question

You invest $50 and it doubles every year. Write an equation to model your investment

Answer 1

we can look at this as an exponential growth, and if something is P today and next year is 2P, hell it doubled and then 4P and so on, so doubling is implying that, whatever P is, will be twice that much in a year, or we can word it as, it'll be 100% more than what it's today, that said, we can just write a Growth equation for "t" years with an annual rate of 100%.

`\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to (100)/(100)\dotfill &1\\ t=years \end{cases} \\\\\\ A = 50(1 + 1)^(t) \implies A = 50(2)^t`