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Troyanec [42]
3 years ago
10

I need help with both a and b please

Mathematics
1 answer:
Anika [276]3 years ago
6 0
A.
2.718... between 2 and 3
2 = √4 and 3 = √9
So, 2.718... between √4 and √9        [√4 < e < √9]


b.
π = 3.1415...
3.1415... between 3 and 4
3 = √9 and 4 = √16
So, 3.1415... between √9 and √16       [√4 < π < √9]
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Answer:

y=8 \cdot (\frac{5}{4})^x

f(x)=8 \cdot (\frac{5}{4})^x

or

f(x)=8 \cdot (1.25)^x

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

y=a \cdot b^x, (b\neq 0).

If you are given the y-intercept, then a is easy to find.

It is just the y-coordinate of the y-intercept is your value for a.

(Why? The y-intercept happens when x=0. Replacing x with 0 gives y=a \cdot b^0=a \cdot 1=a. This says when x=0 \text{ that} y=a.)

So a=8.

So our function so far looks like this:

y=8 \cdot b^x

Now to find b we need another point. We have two more points. So we will find b using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given (1,10) is a point on our curve.

So when x=1, y=10.

10=8 \cdot b^1

10=8 \cdot b

Divide both sides by 8:

\frac{10}{8}=b

Reduce the fraction:

\frac{5}{4}=b

So the equation if it works out for the other point given is:

y=8 \cdot (\frac{5}{4})^x

Let's try it.  So the last point given that we need to satisfy is (2,12.5).

This says when x=2, y=12.5.

Let's replace x with 2 and see what we get for y:

y=8 \cdot (\frac{5}{4})^2

y=8 \cdot \frac{25}{16}

y=\frac{8}{16} \cdot 25

y=\frac{1}{2} \cdot 25}

y=\frac{25}{2}

y=12.5

So we are good. We have found an equation satisfying all 3 points given.

The equation is y=8 \cdot (\frac{5}{4})^x.

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Step-by-step explanation:

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Answer:

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6 - 5x + 7 - 2x = 90

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