For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. y=300(1−t)^5

Emeli Hagan
2021-09-13
Answered

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yunitsiL

Answered 2021-09-14
Author has **108** answers

Remember the formula for an exponential function is represented by
$f\left(x\right)=a{b}^{x}$
where a is the initial value and @ is the growth rate.

If the base, b > 1, then it shows exponential growth. If it is 0 <b <1, then it shows exponential decay.

Note that the base is an independent variable in the function. Therefore, this equation neither represents exponential growth nor exponential decay.

If the base, b > 1, then it shows exponential growth. If it is 0 <b <1, then it shows exponential decay.

Note that the base is an independent variable in the function. Therefore, this equation neither represents exponential growth nor exponential decay.

asked 2022-06-13

The tensor product of two vector spaces U and V is defined as the dual of the vector space of all the bilinear forms on the direct sum of U and V. Is there a generalised form of this for the direct sums of more than two vector spaces? Is there a relation between the space of all multilinear forms on the direct sum of ${V}_{1}$,${V}_{2}$,${V}_{3}$,...,${V}_{k}$ with their tensor product.

Please explain without invoking other algebraic objects such as modules,rings etc and by using the concepts regarding vector spaces only (as the book assumes no such background either, it is unlikely that any reader of that book will benefit from such an exposition). Everywhere I searched, I found the explanation in terms of those concepts only and being unfamiliar to those I couldn't get them at all. Thanks in advance.

Please explain without invoking other algebraic objects such as modules,rings etc and by using the concepts regarding vector spaces only (as the book assumes no such background either, it is unlikely that any reader of that book will benefit from such an exposition). Everywhere I searched, I found the explanation in terms of those concepts only and being unfamiliar to those I couldn't get them at all. Thanks in advance.

asked 2021-09-17

Given:

n=3;

4 and 2i are zeros;

f(-1)=75

Find an nth-degree polynomial function with real coefficients

n=3;

4 and 2i are zeros;

f(-1)=75

Find an nth-degree polynomial function with real coefficients

asked 2021-05-03

Explain how transformations, families of functions, and parent functions are related.

asked 2022-06-13

Is there a genuinely respectable published expository account of what power series are used for, of which a substantial portion would be comprehensible to those first learning of power series in a first-year calculus course?

(I think it's a flaw in the way mathematics is conventionally taught that one first learns answers to questions like this only by taking a later course for which the one introducing the concept is a prerequisite, and one has no prior notice of which course that might be. And in the case of power series, there are many such courses, but still very few compared to the number of courses a student might later take, so the situation is worse.)

(I think it's a flaw in the way mathematics is conventionally taught that one first learns answers to questions like this only by taking a later course for which the one introducing the concept is a prerequisite, and one has no prior notice of which course that might be. And in the case of power series, there are many such courses, but still very few compared to the number of courses a student might later take, so the situation is worse.)

asked 2022-07-04

Often when I'm working on a math problem, there comes a point when I've set everything up and what remains is to expand some expression, substitute something in, solve an equation, or otherwise enter the domain of algebra.

I find that I usually think about this step in the problem as a black box, into which I put a set of equations and out of which comes a set of solutions. This is particularly true if the algebra involved includes many steps.

This is good in a lot of ways and bad in some others, but putting that aside, I'm fascinated that this step seems to come up in all areas of math. Is it possible to separate math from algebra? Are there any branches of math where long chains of algebra are not found or uncommon?

I find that I usually think about this step in the problem as a black box, into which I put a set of equations and out of which comes a set of solutions. This is particularly true if the algebra involved includes many steps.

This is good in a lot of ways and bad in some others, but putting that aside, I'm fascinated that this step seems to come up in all areas of math. Is it possible to separate math from algebra? Are there any branches of math where long chains of algebra are not found or uncommon?

asked 2021-03-05

To calculate: To write the given statements (a) and (b) as functions f(x) and g(x)respectively.

Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test.

One problem worth 8 points had insufficient data, so nobody could solve that problem.

The professor adjusted the grades for the class by

a. Increasing everyones

Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test.

One problem worth 8 points had insufficient data, so nobody could solve that problem.

The professor adjusted the grades for the class by

a. Increasing everyones

asked 2021-08-03

Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each functions