Mathematics: What is a exponential function

What is a exponential function, №9843711, 14.05.2020 01:14

Mathematics

for every increase of 1 on the richter scale, an earthquake is 10 times more powerful. which of the following models this situation? a-linear function with a negative rate of change b- linear function with a positive rate of change c-exponential decay function d-exponential growth function answer-exponential growth function

Step-by-step answer

P Answered by PhD

43

That's an exponentially growing function.

Mathematics

for every increase of 1 on the richter scale, an earthquake is 10 times more powerful. which of the following models this situation? a-linear function with a negative rate of change b- linear function with a positive rate of change c-exponential decay function d-exponential growth function answer-exponential growth function

Step-by-step answer

P Answered by PhD

43

That's an exponentially growing function.

Mathematics

Each time a tennis ball is used, its pressure is 999/1,000 what it was after the previous use -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

B

Step-by-step explanation:

Looking at the problem, we see that our constant rate is 999/1000 because the pressure is only nine hundred ninety-nine hundredths of the previous pressure. Since this is a rate, it can't be a linear function, so eliminate C.

Now, look at the rate. 999/1000 < 1, which means that the function is decreasing as the x values approach infinity or grow larger. That is an indication that this is an exponential decay.

The answer is thus B.

Mathematics

The quantity of detergent in a liter of groundwater near an industrial area is expected to increase by 0.05 grams per year. -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

1

C. Linear

Step-by-step explanation:

The problem says that the quantity will increase each year, so we can definitely get rid of exponential decay because that indicates that the graph will decrease.

Now, the problem says the quantity increases 0.05 grams per year. It doesn't say anything about multiplication or how one year's quantity is k times the previous year's quantity. That means this must not be exponential at all, eliminating A.

Instead, this is actually linear because the common difference that you add each year is 0.05.

The answer is thus C.

Mathematics

A star becomes twice as bright every 10 years -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

1

A

Step-by-step explanation:

"Twice" as bright can translate into the mathematical expression "times 2", where for every year, you multiply the previous year's brightness by 2.

Since this is a rate (using multiplication) and not a common difference (not using addition), it must be an exponential something, so eliminate C.

Now, since 2 > 1, that means this is an exponential growth. Remember that if the rate r is less than 1, then it's decay; if r is greater than 1, then it's growth.

The answer is thus A.

Mathematics

The quantity of detergent in a liter of groundwater near an industrial area is expected to increase by 0.05 grams per year. -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

1

C. Linear

Step-by-step explanation:

The problem says that the quantity will increase each year, so we can definitely get rid of exponential decay because that indicates that the graph will decrease.

Now, the problem says the quantity increases 0.05 grams per year. It doesn't say anything about multiplication or how one year's quantity is k times the previous year's quantity. That means this must not be exponential at all, eliminating A.

Instead, this is actually linear because the common difference that you add each year is 0.05.

The answer is thus C.

Mathematics

A star becomes twice as bright every 10 years -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

1

A

Step-by-step explanation:

"Twice" as bright can translate into the mathematical expression "times 2", where for every year, you multiply the previous year's brightness by 2.

Since this is a rate (using multiplication) and not a common difference (not using addition), it must be an exponential something, so eliminate C.

Now, since 2 > 1, that means this is an exponential growth. Remember that if the rate r is less than 1, then it's decay; if r is greater than 1, then it's growth.

The answer is thus A.

Mathematics

A ship embarked on a long voyage. At the start of the voyage, there were 300 ants in the cargo hold of the ship. One week into the voyage, there were 600 ants. Suppose the population of ants is an exponential function of time. (Round your answers to two decimal places.) How long did it take the population to double? weeks How long did it take the population to triple? weeks When were there 10, 000 ants on board? weeks There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 anteaters, and

Step-by-step answer

P Answered by PhD

The answers to the question are

How long did it take the population to double? Answer = one weekHow long did it take the population to triple? Answer = 1.58 weeksWhen were there 10, 000 ants on board? Answer = 5.06 weeksHow long into the voyage were there 200 ants per anteater? Answer = 11.38 weeks

Step-by-step explanation:

To solve the question we use a similar analogy of half life calculation

Therefore we have

$N_{(t)} =N_{(0)}(2 )^{\frac{1}{t} }$ where

$N_{(t)} =$ Number of ants after time t

$N_{(0)} =$ Starting number of ants

Therefore

600 = 300 × $2^{\frac{1}{t} }$

$2^{\frac{1}{t} }$ = 2

㏑ $2^{\frac{1}{t} }$ = ㏑2

$\frac{1}{t}$ ㏑2 = ㏑2

$\frac{1}{t}$ = 1 and t = 1 week

It took one week for the population of the ants to double

For the population to triple, we have

3×300 = 300× $2^{\frac{x}{1} }$

900 = 300× $2^{\frac{x}{1} }$

$2^{\frac{x}{1} }$ =3

x㏑2 =㏑3 or x = $\frac{ln3}{ln2}$ = 1.58 weeks

There were 10000 ants onboard after

10000 = 300× $2^{x }$

or $2^{x }$ = $\frac{100}{3}$ and x = (㏑ $\frac{100}{3}$ )/㏑2 = 5.06 weeks

For the anteaters we have

Time for the anteaters to double = 3.2 weeks

Therefore t in the equation $N_{(t)} =N_{(0)}(2 )^{\frac{1}{t} }$ = 3.2 weeks

and the length of time it took for the population of ant eaters to grow to 200 is given by

200 = 17× $2^{\frac{x}{t} }$ =17× $2^{\frac{x}{3.2} }$

From which we have

$\frac{x}{3.2}$ ㏑2 = ㏑(200/17)

x = 3.2×3.56 = 11.38 weeks

Mathematics

Each time a tennis ball is used, its pressure is 999/1,000 what it was after the previous use -Exponential growth -Exponential decay -Linear -None of the above

Step-by-step answer

P Answered by PhD

B

Step-by-step explanation:

Looking at the problem, we see that our constant rate is 999/1000 because the pressure is only nine hundred ninety-nine hundredths of the previous pressure. Since this is a rate, it can't be a linear function, so eliminate C.

Now, look at the rate. 999/1000 < 1, which means that the function is decreasing as the x values approach infinity or grow larger. That is an indication that this is an exponential decay.

The answer is thus B.

Mathematics

A ship embarked on a long voyage. At the start of the voyage, there were 300 ants in the cargo hold of the ship. One week into the voyage, there were 600 ants. Suppose the population of ants is an exponential function of time. (Round your answers to two decimal places.) How long did it take the population to double? weeks How long did it take the population to triple? weeks When were there 10, 000 ants on board? weeks There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 anteaters, and

Step-by-step answer

P Answered by PhD

It takes 1 week for the ant population to double

It takes 1.58 weeks for the ant population to triple

It takes 5.06 weeks for the ant population to reach 10000

It takes 5.09 weeks for the ant population to be 200 times the ant eater population.

Step-by-step explanation:

It takes only 1 week for the population to double from 300 to 600

We can model the population of ant (or anteater) as the following: