Hi I was wondering how to create an equation of the form y=Ae to the power of Bx using the values in the table

Question

Hi I was wondering how to create an equation of the form y=Ae to the power of Bx using the values in the table. X values are 0,1,2,3,4,5,6,7 and the log y values are 0.693, 1.193, 1,693, 2.193, 3.193, 3.693, and 4.193. it also says to validate your response mathematically.
Thanks any help would be awesome

Answer 1

Hello Aj,

 

The first thing we have to remember is

 

log_bx = n 

 

bⁿ = x

 

y = Ae^Bx

log_ey = log_e(Ae^Bx)

Since log(cd) = log c + log d, we can rewrite the equation above as

log_ey = log_eA + log_e(e^Bx)

log_ey = log_eA + Bx

 

We have the following table of values

x      log_ey

0     0.693

1     1.193

2     1.693

3     2.193

4     3.193

5     3.693

6     4.193

 

We can use these values to solve for A and B.  Note that log_e = ln and it's just easier to type.

lny = lnA + Bx

 

Using x=0 we can solve for A

0.693 = lnA + B(0)

0.693 = lnA

e^0.693 = e^lnA = A

A = 2

 

Using A = 2 and another (x, lny) pair, we can solve for B

lny = lnA + Bx

1.193 = ln2 + B(1)

1.193 = .693 + B

B = .5

 

Using these values, we can restate our original equation

y = 2e^0.5x