What is 1/2b^2-b in factored form ?

Suppose f is a function with exponential growth and f(0)=1. Explain why f can be represented by a formula of the form

galben [10]

We are supposed to explain why the given function can be expressed in form $f(x)=b^{x}$ , when $f(0)=1$ .

Since the given function is an exponential function we can express it as $f(x)=a(b)^{x}$ .

Now let us substitute x=0 in the given function,

$f(x)=b^{x}$

$f(0)=b^{0}$

$f(0)=1$

Let us substitute x=0 in our function.

$f(0) = a(b)^{0}$

$f(0) = a\cdot 1$

$f(0)=a$

Upon substituting a=1 in our function we will get,

$f(x) = 1(b)^{x}$

$f(x) =(b)^{x}$

Therefore, our function f can be represented by the formula of the form $f(x)=b^{x}$ .

7 0

3 years ago

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Guys help.. this is overdue..

loris [4]

So if his homework takes 25 minutes , and his math takes m minutes , and then as a while it takes h minutes, here’s an example of two equations you can use ;
M+25= h of 25+m=h you can do either one as you please because it doesn’t matter the order as long as they
Both equal h !! Hope this helps , sorry that it’s overdue :( have a great day:))))

4 0

2 years ago

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Help ill give u 25 points

atroni [7]

Answer:

I need points

Step-by-step explanation:

I'm so so sorry

3 0

3 years ago

I need help with this question can someone please help me?

zlopas [31]

Answer: y= -1/1x - 1

Okay, to find the equation you must find the y-intercept and the slope.

To find the y-intercept, you must find (0,y). This is the point on the y-axis where x is 0. So, where along the y-axis is there a point? There is a point at (0,-1). Therefore, your y-intercept is -1.

To find the slope, you must do rise/run. Go to a point on the line, such as (0,-1). You must go up (or down) until you get lined up with next point on the line. You go up one time. Then, you must go right (or left) to get to the exact point. In this case, the point would be (-1,0). You go left one time.

If you go down or left when doing rise/run, the number would be negative. Since you went left, that number would be negative.

So, our slope would be 1/-1, which can also be written as -1/1.

Now, write the equation. There is always an x next to the slope. y= -1/1x

Then, put the y-intercept next to it. If it is positive, use a +. If it is negative, use a -. It is negative.

Therefore, the answer is y= -1/1x -1.

5 0

2 years ago

In order to help identify baby growth patterns that are unusual, we need to construct a confidence interval of the mean head cir

sukhopar [10]

Answer:

The 99% confidence interval estimate of the mean head circumference of all 2-month-old babies is (40.18cm, 41.02cm).

Step-by-step explanation:

Our sample size is 100.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 100-1 = 99$ .

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-\alpha}{2} = \frac{0.01}{2} = 0.005$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 99 and 0.005 in the t-distribution table, we have $T = 2.626$

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{1.6}{\sqrt{100}} = 0.16$

Now, we multiply T and s

$M = Ts = 2.626*0.16 = 0.42$

For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is

$L = 40.6 - 0.42 = 40.18$ cm

For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is

$L = 40.6 + 0.42 = 41.02$ cm

So

The 99% confidence interval estimate of the mean head circumference of all 2-month-old babies is (40.18cm, 41.02cm).

3 0

3 years ago