# Find Expontntial Model that fits the points shown in the graph of table01510102841.jpg

Find Expontntial Model that fits the points shown in the graph of table

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odgovoreh

Let us consider the following exponential model
$y=a{e}^{x}$
Now, with given point (0,5), the equation becomes
$5=a{e}^{b\left(0\right)}$
$5=a{e}^{0}$
Therefore,
$a=5$
With the given point (4,1) and $a=1$, the equation becomes
$1=5{e}^{b\left(4\right)}$
Dividing both sides by 5
$\frac{1}{5}={e}^{4b}$
Taking natural logarithm to the base e
$\frac{\mathrm{ln}1}{5}={\mathrm{ln}e}^{4b}$
Using the inverse property ${\mathrm{ln}e}^{x}$
$\frac{\mathrm{ln}1}{5}=4b$
Therefore,
$b=\frac{\frac{\mathrm{ln}1}{5}}{4}$
$b=-0.4024$
Hence, the equation of the curve with $a=5$ and $b=-0.4024$ is $y={e}^{-0.4024x}$