Posted by **maths help** on Saturday, January 2, 2010 at 8:12am.

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 -
**drwls**, Saturday, January 2, 2010 at 8:25am
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 -
**Reiny**, Saturday, January 2, 2010 at 8:25am
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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