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4 years ago

9

Given the exponential function f(x) = 16(0.75)x, classify the function as exponential growth or decay and determine the percent

rate of growth or decay.

2 answers:

zzz [600]4 years ago

4 0

Answer: it's Exponential decay, 75% decrease

Step-by-step explanation: since Exponential decay is when base of the exponent is between 1 and 0. (0.75) is decay. then you move the decimal back twice.

vagabundo [1.1K]4 years ago

3 0

Answer:

The answer is Exponential decay, 25% decrease

Step-by-step explanation:

In f(x) = 16(0.75)x the (0.75) does not have a 1 so it is decreasing and if it is only 75% of 16 then it would be losing 25% each time

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A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 ho

emmasim [6.3K]

Answer:

The equation in point slope form is $y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)$

Step-by-step explanation:

Since the swimming pool is being drained at a constant rate, the equation of the process must be a first-order polynomial (linear function), where depth of water decrease as time goes by. The form of the expression is:

$y = m \cdot t + b$

Where:

$t$ - Time, measured in hours.

$b$ - Initial depth of the water in swimming pool (slope), measured in inches.

$m$ - Draining rate, measured in inches per hour.

$y$ - Current depth of the water in swimming pool (x-Intercept), measured in inches.

If $m = -3\,\frac{in}{h}$ and $y (5\,h) = 32\,in$ , the initial depth of the water in swimming pool is:

$b = y - m\cdot t$

$b = 32\,in -\left(-3\,\frac{in}{h} \right)\cdot (5\,h)$

$b = 47\,in$

The equation in point slope form is:

$y-y_{o} = m \cdot (t-t_{o})$

Where $y_{o}$ and $t_{o}$ are initial depth of the water in swimming pool and initial time, respectively. Then, the equation in point slope form is:

$y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)$

7 0

3 years ago

On a map, the distance of two inches is equal to ten miles. How many miles does 4 inches represent on the map?

dybincka [34]

20 miles is the answer

6 0

3 years ago

The president of the student council wants to survey the student population about parking. She decides to use a random number ta

Advocard [28]

Answer:

0759, 1019

Step-by-step explanation:

Edge 2020/2021

3 0

3 years ago

Read 2 more answers

Choose the answer to complete each statement

Stolb23 [73]

Answer:

Slope: -7/-3=7/3x

Y-int: -3

Function: y=7/3x-3

4 0

3 years ago

A data set includes 103103 body temperatures of healthy adult humans having a mean of 98.998.9degrees°f and a standard deviation

dangina [55]

Answer:

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=98.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.65 represent the sample standard deviation

n=103 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=103-1=102$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,102)".And we see that $t_{\alpha/2}=2.62$

Now we have everything in order to replace into formula (1):

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

6 0

3 years ago

Read 2 more answers