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a diagram shows the (exponential)graph of y=3e^kx. the graph goes through the points (0,3) and (4,18).

what is the value of k?

is it:
a)3/2e

b)1/4 log(smalle)6

c) 1/4 log(smalle)15

d) 1/18 log(smalle)4/3

could you please go over the working because i have no clue what to do...many thanks in advance

  • maths -

    Require that y = 3 when x = 0, in order go through the point (0,3). Solve the resulting equation for k, and ALSO make sure the line also goes through the other point.
    3 = 3e^(k*0) = 3
    This is valid for any k, so it doesn't help at all. Now trying making if go through the other point.
    18 = 3e^(4k)
    e^(4k) = 6
    4k = ln 6
    k = (ln6)/4
    which is choice b.

  • maths -

    Substitute (4,18) into the equation

    18 = 3e^(4k)
    6 = e^(4k)
    take ln of both sides
    ln6 = ln(e^(4k))
    ln6 = 4k(lne), but lne = 1
    ln6 = 4k
    k = ln6/4 or the choice of (1/4)lne

    (subbing the point (0,3) gains us nothing, since it would be true for any value of k)

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