# exponential and logarithmic graphs question

hi, i desperately need help solving this question:

Find the values of A and k if the general equation of the graph shown is y=Ae^kx where the graph goes through the points (-1,-4) and (-2,-10)

do i solve it using simultaneous equations? because i have attempted this yet failed :/

Try taking logs of both sides first, after multiplying both sides by -1 (to avoid logs of negative numbers).
ln (-y) = ln (-A) + kx
ln (4) = ln (-A) -k
ln (10) = ln (-A) -2k
-k = ln 10 - ln 4 = 0.91629
k = -0.91629
ln 4 = ln(-A)+0.91629
ln (-A) = 0.47000
A = -1.6000
y = -1.6 e^(-0.91629 x)

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asked by elle

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