Question

find a formula for an exponential function passing through the points (2.5), (6,9)

Answer 1

General formula is y=b*a^x.

If you set x=2, y=5 and x=6, y=9 you get two equations with two variables (a and b).
Solve this system to get your function.

Answer 2

You can also take another approach: exponential means every time x increases 1, y is multiplied with a.
Given the points (2, 5) and (6, 9), you take four steps (from 2 to 6) and go from 5 to 9.

This means: 5*a*a*a*a=9, because every time x increases 1, you multiply with a.

In short: 5*a^4=9, so a^4=9/5.

From this you can calculate a.
Once you've got a, put it in the formula and calculate b.

Answer 3

i am sorry but i do not understand this at all

Answer 4

In an exponential function, every time your x increases 1 unit, your y-value is multiplied with the same number.

e.g. y=2^x.

If x=3, then y=2^3=8
if x=4, y=2^4=16 (=8*2)
if x=5, y=2^5=32 (=16*2)
if x=6, y=2^6=64 (=32*2)

See? every time x increases 1 unit, y is multiplied with 2.

Answer 5

Then you have to ask yourself: do I know the general form of an exponential function?

It is y = b*a^x

In the example it was y=2^x, which could be written as

y=1*2^x,

so b=1 and a=2.

Now you do know your function is exponential, but you only have two points that lie on the graph: (2, 5) and (6, 9). For many people it is hard to believe that there is now only one possible exponential function with those points on its graph.

If you reread what I explained about finding a, you may understand better now, I hope...

Answer 6

so a will=1.158

Answer 7

Yes! Well done.

Answer 8

so b= 30.06

Answer 9

and the equation will y=(1.158)(30.06)^x

Answer 10

I got: b= 5/1.158^2=3.727

Answer 11

thank you .. i know where i messed up i was using the same points.. i get.. thank you so much for ur help.. u r awesome

Answer 12

YW!