A diagram shows a straight line graph of In y against x,passing through the point (0,2) and having gradient -3/2 .

Question

The variables x and y are connected by the equation y=pq^x ,where p and q are constants
Find
(i)the value of p and of q ,to one decimal place
(ii)the equation relating x and y

Answer 1

y = pq^x
lny = lnp + x lnq

2 = lnp + 0 lnq
p = e^2

1/y y' = lnq
y' = y ln q
-3/2 = 2 lnq
lnq = -3/4
q = e^(-3/4)

y = e^2 e^(-3x/4)

Answer 2

Can be more specific? still do not understand ...
The answer for part (ii) should be y=7.4(0.2)^2
and the values of q is o.2 ..

Answer 3

sorry. Guess I should not have given that last line, but the values for p and q were given...

p = e^2 = 7.4
q = e^(-3/2) = 0.2