How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?

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How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?

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Answer 1 · 2016-06-08T22:37:20

We know the value of $(x, y)$ $(x, y)$ in two different cases. Therefore, we need to find the value of a and b. We have enough information to write a system of equations and to solve for a and b.

Explanation:

$\frac{2}{5} = a \times b^{- 1}$ $2/5= a xx b^(-1)$

$2 = a \times b^{0}$ $2 = a xx b^0$

$2 = a \times 1$ $2 = a xx 1$

$2 = a$ $2 = a$

$\frac{2}{5} = 2 \times \frac{1}{b}$ $2/5 = 2 xx 1/b$

$\frac{2}{5} = \frac{2}{b}$ $2/5 = 2/b$

$b = 5$ $b = 5$

The equation of this function is therefore $y = 2 \times 5^{x}$ $y = 2 xx 5^x$ .

Hopefully this helps!

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How do you find an exponential function of the form f(x)=ab^x that has the given y-intercept (0,2); passing through P=(-1, 2/5)?

1 Answer

Explanation:

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