Exponential Function

Question

Find a formula for an exponential function that passes through the points (0,5) and (3,40).

Answer 1

You can set this up as a system of 2 equations in 2 unknowns.

 

y = ca^x

 

The 2 points let you write 2 equations.

 

(0,5) gives you 5 = ca⁰ = c(1) = c

 

Now use c = 5 and the other point.

 

(3,40) and c = 5 give you

 

40 = 5a³

 

a³ = 8

 

a = 2

 

Final function:  y = 5(2^x)

Answer 2

Cassie,

 

Sometimes exponential functions can be quite easy to work 

with, especially if you know what the variables do to the graph.

 

Here is how I would work your problem:

 

y = ab^x     Standard exponential equation where:

 

a = y-intercept

 

b = multiplier or common ratio between two consecutive

      integral y values

 

You must have numeric values for a and b in your equation

 

( 0 , 5)  ( 3 , 40 ) lie on the graph; 

 

5 is the y-intercept and therefor a = 5

 

      y = 5 b^x

 

to go from (0,5) to (3,40) the b would be used 3 times

 

  40 = 5 b³

 

   8 = b³

 

   2 = b

 

So your exponential equation is:  y = 5 (2^x)

Answer 3

 

When working with exponential functions, it is often useful to work with the equation in “base-intercept” form:

 

y = y₀ * a^x

 

The point (0, 5) gives y₀

When x = 0, a^x = 1

 

y = 5 * a^x

 

Using the point (3, 40)

 

40 = 5 * a³

 

40/5 = 8 = a³

 

₃√8 = 2

 

a = 2

 

then your Eq. is;

 

y = 5 ( 2^x )

Answer 4

An exponential function:

f(x) = b^x

If (0, 5) is a solution:

f(0) = b⁰

5 ≠ 0!

 

Check the accuracy of the information.