2 years ago

Question 1

Mathematics

2 answers:

Svetach [21]2 years ago

5 0

The answer to the question is $5.40

diamong [38]2 years ago

4 0

$5.40 is the correct answer

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Find the formula for an exponential function that passes through the two points give.

Ksenya-84 [330]

Answer:

$y=3(2)^{x}$

Step-by-step explanation:

Given.

Two points are given.

$(x, y)=(-1,\frac{3}{2})$ and $(x, y)=(3,24)$

An exponential function is in the general form.

$y=a(b)^{x}$ -------(1)

We know the points $(-1,\frac{3}{2})$ and $(3,24)$

put the first point value in equation 1

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

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

$a=\frac{3}{2}\times b$ --------(2)

put the second point value in equation 1

$24=a(b)^{3}$ ----------(3)

Put the a value from equation 2 to equation 3

$24=\frac{3}{2}\times b(b)^{3}$

$b^{3+1}=\frac{24\times 2}{3}$

$b^{4} = 16\\b=\sqrt[4]{16} \\b=2$

Put the b value in equation 2

$a=\frac{3}{2}\times 2$

$a=3$

Put the a and b value in equation 1

$y=3(2)^{x}$

So, the exponential function that passes through the points $(-1,\frac{3}{2})$ and $(3,24))$ are $y=3(2)^{x}$ .

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