Find the equation of an exponential curve that passes through #(1,4)# and #(2,36)#?

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Answer 1 · 2017-12-14T11:37:34

# a=4/9 # and # b = ln 9 #

Thus the equation is:

# y = 4/9e^(xln9) #

Assuming the relationship:

# y = ae^(bx) #

This has two unknowns and we are given two coordinates:

For coordinate #(1,4)#:

# 4 = ae^(b) # ..... [A]

For coordinate #(2,36)#:

# 36 = ae^(2b) # ..... [B]

Eq [B] #divide# Eq [A]:

# 36/4 = ( ae^(2b) ) / ( ae^(b) ) #
# :. 9 = e^(b) #
# :. b = ln 9 #

Substitute for #b# in Eq[A]:

# 4 = ae^(ln9) #
# :. 4 = 9a #
# :. a=4/9 #

Thus the equation is:

# y = 4/9e^(xln9) #

graph{4/9e^(x*ln9) [-20, 20, -10, 45]}