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!