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younganastasia1

younganastasia1

09.06.2021 •

Mathematics

I’m so confused on how to find the answer to this

I’m so confused on how to find the answer to this

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Ответ:

tiffanibell71

09.06.2021

Step-by-step explanation:

download an app called algebrator its way easier than asking

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Ответ:

drew1t

13.09.2022

$f(x) = \frac{24}{25} * \frac{5}{6}^x$

Step-by-step explanation:

Given

$(x_1,y_1) = (2,\frac{2}{3})$

$(x_2,y_2) = (3,\frac{5}{9})$

Required

Write the equation of the function f(x) = ab^x

Express the function as:

y = ab^x

In: $(x_1,y_1) = (2,\frac{2}{3})$

y = ab^x

$\frac{2}{3} = a * b^2$ --- (1)

In $(x_2,y_2) = (3,\frac{5}{9})$

y = ab^x

$\frac{5}{9} = a * b^3$ --- (2)

Divide (2) by (1)

$\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}$

$\frac{5}{9}/\frac{2}{3} = b$

$\frac{5}{9}*\frac{3}{2} = b$

$\frac{5}{3}*\frac{1}{2} = b$

$\frac{5}{6} = b$

$b = \frac{5}{6}$

Substitute 5/6 for b in (1)

$\frac{2}{3} = a * b^2$

$\frac{2}{3} = a * \frac{5}{6}^2$

$\frac{2}{3} = a * \frac{25}{36}$

$a = \frac{2}{3} * \frac{36}{25}$

$a = \frac{2}{1} * \frac{12}{25}$

$a = \frac{24}{25}$

The function: f(x) = ab^x

$f(x) = \frac{24}{25} * \frac{5}{6}^x$

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