A mathematical model has an equation $y = a e^{b x}$ $y = ae^(bx)$ and this curve passes through the points $A (0, \frac{1}{2})$ $A(0,1/2)$ and $B (4, 5)$ $B(4,5)$ . Find a and b?

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Answer 1 · 2017-09-18T19:25:50

$a = \frac{1}{2}$ $a = 1/2$ and $\frac{1}{4} ln 10$ $1/4ln10$

With these results we have:

$y = \frac{1}{2} e^{(\frac{1}{4} ln 10) x}$ $y = 1/2e^((1/4ln10)x)$

We have:

$y = a e^{b x}$ $y = ae^(bx)$

as a model. And we have two data points:

$A (0, \frac{1}{2})$ $A(0,1/2)$ and $B (4, 5)$ $B(4,5)$

Using $A$ $A$ we have:

$\frac{1}{2} = a e^{0} \to a = \frac{1}{2}$ $1/2 = ae^(0) -> a = 1/2$

Using $B$ $B$ we have:

$5 = \frac{1}{2} e^{b 4} \Rightarrow e^{4 b} = 10$ $5 = 1/2e^(b4) => e^(4b) = 10$
$:. 4b = ln10$
$:. b = 1/4ln10$

With these results we have:

$y = 1/2e^((1/4ln10)x)$

Which we can see graphically:

Steve M

A mathematical model has an equation y = ae^(bx)y=aebxy = ae^(bx) and this curve passes through the points A(0,1/2)A(0,12) A(0,1/2) and B(4,5) B(4,5)B(4,5) . Find a and b?