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3 years ago

Describe a method for writing an exponential equation given a graph

Mathematics

1 answer:

Dominik [7]3 years ago

3 0

Explanation:

We can find the parameters of the exponential equation ...

y = a^(x-h) +k

1. Locate the horizontal asymptote. The y-value of that is the value of k.

2. Locate the point that is at y = k+1. The x-value of that is the value of h.

3. Locate the point that is at x = h+1. Subtract k from the y-value of that to find "a".

____

You have identified the three points on any exponential curve y = a^(x -h) +k. They are ...

(-∞, k) for growth, or (∞, k) for decay

(h, k+1)

(h+1, k+a) . . . . . for decay, (h -1, k+1/a) might be easier to find

_____

Comment on reflected curves

If the curve extends below the horizontal asymptote, it has been reflected about the x-axis. Reflect it across the x-axis, perform the above steps, then multiply the right side of the equation by -1.

_____

Additional note

If the value of h is not an integer, it might be easier to express the curve in the form ...

y = a·b^x +k

In this case, you can find the value of b by finding the y-values associated with three consecutive values of x. Call them (x, y1), (x+1, y2), (x+2, y3). Then ...

b = (y3 -y2)/(y2 -y1)

a = (y1 -k)/b^x . . . . . where x is the x-value of the first point, (x, y1)

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A bag contains five batteries, all of which are the same size and are equally likely to be selected. Each battery is a differen

Cerrena [4.2K]

Answer:

Step-by-step explanation:

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3 years ago

Jerry is 8 years younger than Patricia. Six years ago, Patricia was 3 times as old as Jerry was then. Which system of equations

MissTica

Jerry is 8 years younger than Patricia, so: (1): Jerry = Patricia - 8 Six years ago, Patricia was 3 times as old as Jerry was then, so: (2): (Patricia - 6) = (Jerry - 6)*3 Putting equation 1 in to equation 2 (Patricia - 6) = (Patricia - 8 - 6)*3 Patricia - 6 = 3Patricia - 42 36 = 2Patricia Patricia = 18 And so Jerry = 10

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3 years ago

A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between

lana [24]

Answer:

63% of the values lies between 70 and 85.

Step-by-step explanation:

We are given that a normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97.

Let X = Set of numbers

The z-score probability distribution for is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean value = 75

$\sigma$ = standard deviation = 7.97

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, percentage of values that lies between 70 and 85 is given by = P(70 < X < 85) = P(X < 85) - P(X $\leq$ 70)

P(X < 85) = P( $\frac{ X -\mu}{\sigma}$ < $\frac{ 85-75}{7.97}$ ) = P(Z < 1.25) = 0.89435 {using z table}

P(X $\leq$ 70) = P( $\frac{ X -\mu}{\sigma}$ $\leq$ $\frac{ 70-75}{7.97}$ ) = P(Z $\leq$ -0.63) = 1 - P(Z < 0.63)

= 1 - 0.73565 = 0.26435

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 and x = 0.63 in the z table which has an area of 0.89435 and 0.73565 respectively.

Therefore, P(70 < X < 85) = 0.89435 - 0.26435 = 0.63 or 63%

Hence, 63% of the values lies between 70 and 85.

6 0

3 years ago

Use rounding (to the nearest 10) to estimate the product of 3217 X 44.

Lorico [155]

So using whole number rounding I believe the answer you should get would be 141,550 as 3217 x 44 is equals to 141,548 so the answer may be 141,550 since 50 is the closest ten number to 48, with a distance of only 2 numbers.

8 0

3 years ago

Change 04:35 to 12 hours clock time

mote1985 [20]

Answer:

4:35 am

Step-by-step explanation:

change 04:35 to 12 hours clock time

3 0

2 years ago