how do i find the exponential function?

Question

hi i want to ask how i find the exponential function of a graph when the y -int is (0,4) and a given point is (5,10)
y=k*a^x
i need to find k and a
any help is appreciated thanks!

Answer 1

u have 2 points here
(0,4) & (5,10) these 2 points are on the graph so blug them in the function
----------
(0,4)
4= k * a^0
4= k * 1
k=4
so y=4 a^x
-------------------
(5,10)
10=4* a^5
a^5 =10/4 = 2.5
5 log(a) =log 2.5
log a =(log 2.5) /5 =0.0795880017344
a= 10 ^ 0.0795880017344 = 1.201124434

so
y =4 * (1.201124434) ^ x

Answer 2

y-int (0,4) means when x = 0, y = 4:

y = k a^x
4 = k a^0
4 = k (a^0 = 1),

so y = 4 a^x.

similarly, it goes through (5,10) means when x=5, y=10:

y = 4 a^x
10 = 4 a^5
5/2 = a^5
(5/2)^(1/5) = a

Answer 3

From the given info, we have:
4 = k a^0, or 4 = k;
10 = k a^5, or 10 = 4 a^5, or 2.5 = a*5, so a is the fifth root of 2.5.

Answer 4

OK, here's a hint. Hope my memory is good on this one;
it's been a long time! ;)

If you take the log of each side of the equation you have:

log (Y) = log(k * a^X)

with a bit of algebra, this becomes:

log Y = log(k) + log(a^X)
log Y = log(k) + X * log(a)

This last eq'n is now of the form: "[Y] = m [X] + b", the basic linear equation you've probably worked with before.
Note: here [m] = log(a) -- and you need to plot "log(Y)" instead of just "(Y)".

HTH.
- john