All categories

2 years ago

Which statements are true about exponential decay functions check all that apply

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

5 0

Answer:

The correct statements are:

1) The domain is all real numbers.

4) The base must be less than 1 and greater than 0.

5) The function has a constant multiplicative rate of change.

Step-by-step explanation:

Any function in the form f(x)=ab^x, where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.

if b>1 then we get a exponential growth function and

We know that a exponential decay function is given as:

f(x)=ab^x with 0<b<1

Hence, the statements that are true about the exponential decay functions are:

1) The domain is all real numbers.

This statement is true since the function is defined for all the real values.

2) As the input increases, the output increases.

This statement is false since from the graph we could check that the exponential decay function decreases with the increasing value of x.

3) The graph is the same as that of an exponential growth function .

The statement is false since the graph of growth function increases with increasing x and is opposite of the decay function.

4) The base must be less than 1 and greater than 0.

This statement is true.

5) The function has a constant multiplicative rate of change.

This option is true.

Since there is a constant multiplicative rate of change (i.e. b)

melomori [17]2 years ago

3 0

This is the concept of exponential functions; The statements that are correct about the exponential decay functions are:
1. The domain is all real number
4. The base must be less than 1 and greater than 0
5. The function has a constant multiplicative rate of change

You might be interested in

The equation of line is y = x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on ? Why or why not? no, because b

andrew11 [14]

The answer is 2 and 9 because 9 divide by that is 4.5

6 0

2 years ago

Read 2 more answers

On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negat

SpyIntel [72]

Answer:

They are parallel because their slopes are equal

Step-by-step explanation:

8 0

2 years ago

A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st

maxonik [38]

Answer:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

$p_v =2*P(z>1.413)=0.158$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the average tensile strength is different from 5lbs/mm at 10% of signficance

Step-by-step explanation:

Data given and notation

$\bar X=5.0611$ represent the sample mean

$\sigma=0.2803$ represent the population standard deviation for the sample

$n=42$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 5, the system of hypothesis would be:

Null hypothesis: $\mu = 5$

Alternative hypothesis: $\mu \neq 5$

If we analyze the size for the sample is > 30 but and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{5.0611-5}{\frac{0.2803}{\sqrt{42}}}=1.413$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(z>1.413)=0.158$

Conclusion

8 0

2 years ago

Which shows how to solve the equation Three-fourths x = negative 6 for x in one step?

My name is Ann [436]

option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

Step-by-step explanation:

We have , The given expression as Three-fourths x = negative 6 , which can be written as $\frac{3}{4} (x) = -6$ . Now in order to solve this equation in one step , we must notice that coefficient of x must be 1 but it's $\frac{3}{4}$ , Let's make coefficient of x as 1 by multiplying both side of equations by 4/3:

$\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4}(\frac{4}{3} ) (x) = -6(\frac{4}{3} )$

⇒ $x = -6(\frac{4}{3} )$

⇒ $x = -2(4)$

⇒ $x = -8$

Therefore, x= -8 & correct option to solve the equation Three-fourths x = negative 6 for x in one step is option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

7 0

2 years ago

Read 2 more answers

Yi is running for class president. To try to predict how people will vote, she wants to take a poll with a 90% confidence level

slega [8]

90The information that you'd need in determining sample size when the standard deviation is unknown is:

z-value for the given level of confidence ⇒ The level of confidence is 90% and the z-value by convention is 1.645

The margin error (E) = 4%

The proportion of the population that you'd expect to vote for Yi. If this information isn't provided, use 50%. We call this value, p, the probability of success.

The probability of not success is q = 1 - 0.5 = 0.5

STEP 1:
Half the margin error = 0.04 ÷ 2 = 0.02

STEP 2:
Multiply the probability of success by the probability of fail = 0.5 × 0.5 = 0.25

STEP 3:
Divide z-score by half of E = 1.645 ÷ 0.02 = 82.25
Then square the answer = 82.25² = 6765 rounded to the nearest integer)

STEP 4:
Multiply the answer from STEP 2 by the answer from STEP 4
0.25 × 6765 = 1691 (rounded to the nearest integer)

Answer: Minimum Sample Size is 1691

8 0

2 years ago

Read 2 more answers