Doing another problem: Show that the rate of change of is proportional to y. I know that you have to find the derivative & somehow find a constant to place in front of y. Stuck here.
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Originally Posted by zachd77 Doing another problem: Show that the rate of change of is proportional to y. I know that you have to find the derivative & somehow find a constant to place in front of y. Stuck here. what did you get for the derivative of y ?
I got 3^(2x)*(7 ln(5))5^(7x)+5^(7x)*(2 ln(3))9^x... bit messy, best I could do to show y'
$\displaystyle y' = 3^{2x} \cdot 7\ln{5} \cdot 5^{7x} + 5^{7x} \cdot 2\ln{3} \cdot 3^{2x}$ $\displaystyle y' = 3^{2x}5^{7x}(7\ln{5} + 2\ln{3})$ $\displaystyle y' = y(7\ln{5} + 2\ln{3})$
thanks!!
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