bobbie71G

2021-09-22

Find the exponential model $y=a{e}^{bx}$ that fits the points (0, 2) and (4, 3)

SchepperJ

Skilled2021-09-23Added 96 answers

Use the first point to fina a.

$y=a{e}^{bx}$

$2=a{e}^{b\cdot 0}$

$2=a\cdot 1$

$a=2$

Use the second point to find b.

$y=2{e}^{bx}$

$3=2{e}^{4b}$

$\frac{3}{2}={e}^{4b}$

$\mathrm{ln}\frac{3}{2}={\mathrm{ln}e}^{4b}$

$4b=\mathrm{ln}\frac{3}{2}$

$b=\frac{1}{4}\mathrm{ln}\frac{3}{2}$

Write the equation for the exponential model.

$y=2{e}^{\frac{x}{4}\mathrm{ln}\frac{3}{2}}$

Result:$y=2{e}^{\frac{x}{4}\mathrm{ln}\frac{3}{2}}$

Use the second point to find b.

Write the equation for the exponential model.

Result:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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