# Algebra

Construct exponential functiom of points (0,200) and (6,380).

The exponential function is
y(x)=____

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1. let the exponential equation be y = a e^(kx)
for (0,200)
200 = a e^0
a = 200

so you have y = 200 e^kx
for (6,380)
380 = 200 e^(6k)
1.9 = e^(6k)
take ln of both sides, and use rules of logs
ln 1.9 = 6k lne, but lne = 1
6k = ln 1.9
k = ln 1.9/6

the exponential equation is
y = 200 e^(ln1.9/6 x)

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