# A mathematical model has an equation #y = ae^(bx)# and this curve passes through the points # A(0,1/2)# and #B(4,5) #. Find a and b?

##### 1 Answer

Sep 18, 2017

#a = 1/2# and#1/4ln10 #

With these results we have:

# y = 1/2e^((1/4ln10)x) #

#### Explanation:

We have:

# y = ae^(bx) #

as a model. And we have **two** data points:

# A(0,1/2)# and#B(4,5) #

Using

# 1/2 = ae^(0) -> a = 1/2#

Using

# 5 = 1/2e^(b4) => e^(4b) = 10#

# :. 4b = ln10 #

# :. b = 1/4ln10 #

With these results we have:

# y = 1/2e^((1/4ln10)x) #

Which we can see graphically: