# How do you find the exponential model #y=ae^(bx)# that goes through the points (0,1) and (3,10)?

##### 1 Answer

Mar 1, 2017

#### Explanation:

We know two

**Equation 1:**

#1 = ae^(0b)#

**Equation 2:**

#10 = ae^(3b)#

The first equation can be simplified to

Solve for

#10 = 1(e^(3b))#

#10 = e^(3b)#

#ln10 = ln(e^(3b))#

#ln10 = 3blne#

#3b = ln10#

#b = 1/3ln10#

The function therefore has equation

Use the logarithm property

#y = (10^(1/3))^x = 10^(x/3)#

Hopefully this helps!