Paper 3 May/June 2008 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

A certain substance is formed in a chemical reaction. The mass of substance formed $t$ seconds after the start of the reaction is $x$ grams. At any time the rate of formation of the substance is proportional $\left( {20 - x} \right)$. When $t = 0$, $x = 0$ and $\frac{{dx}}{{dt}} = 1$.
a) Show that $x$ and $t$ satisfy the differential equation
$\frac{{dx}}{{dt}} = 0.05\left( {20 - x} \right)$.
b) Find, in any form, the solution of this…