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2 years ago

What is the leading coefficient of the polynomial f(c) defined below? need help asap!

Mathematics

1 answer:

SashulF [63]2 years ago

3 0

Answer: 7

Step-by-step explanation:

The leading coefficient is the number before the term with the highest power in your polynomial. The coefficient is just a number or constant that is before a variable in your expression.

In this case, the highest degree in this polynomial is five. If we look at the coefficient of that term, we see that it is seven.

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What is the equivalent fraction of 4/10?

VashaNatasha [74]

Divide both sides by 2.
2/5
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8 0

3 years ago

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The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5

notsponge [240]

<h2> Question # 1</h2>

Answer:

25 is the factor which grows by between x = 5 and x = 7.

Step-by-step explanation:

Considering the exponential function

$f\left(x\right)\:=\:3\left(5\right)^x$

The growth factor between $x=1$ and $x=3$ is given by:

$\left[3\left(5\right)^3\right]\div \left[3\left(5\right)^1\right]$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^3\right]\::\quad 375$

$\mathrm{Calculate\:within\:parentheses}\:\left[3\left(5\right)^1\right]\::\quad 15$

So,

= $375\div \:15$

= $25$

Similarly, growth factor between $x=5$ and $x=7$ is given by:

$\left[3\left(5\right)^7\right]\div \left[3\left(5\right)^5\right]$

= $\frac{3\cdot \:5^7}{3\cdot \:5^5}$

$\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1$

= $\frac{5^7}{5^5}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{5^7}{5^5}=5^{7-5}$

= $5^{7-5}$

= $5^2$

= $25$

Therefore, 25 is the factor which grows by between x = 5 and x = 7.

<h2> Question # 2</h2>

Answer:

The population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

The graph for $y=A\cdot \left(b\right)^t$ is also shown in attached figure.

Step-by-step explanation:

If a city that currently has a population of 1000 triples in size every 8 years.
what will the population be in 24 years?
Is the population growth modeled by a linear function or an exponential function?

As the city that currently has a population of 1000 triples in size every 8 years.

So, for this case

$y=A\cdot \left(b\right)^t$

where

$A$ = Initial population amount

$b$ = growth rate

$t$ = time

Substituting the values in the function

$y=A\cdot \left(b\right)^t$

$y=1000\cdot \:\:3^{\frac{1}{8}t}$

So, the population be in 24 years

$y=1000\cdot \:\:3^{\frac{1}{8}24}$

$3^{\frac{1}{8}\cdot \:24}=3^3$

$\:y=3^3\cdot 1000$

$y=1000\cdot \:\:27$

$y=27000$

Therefore, the population be in 24 years will be 27000.

Also, the population growth modeled by an exponential function as $y=A\cdot \left(b\right)^t$ is an exponential function.

<h2 /><h2> Question # 3</h2>

Answer:

the graph of the function will translate horizontally 3/5 units right.

Step-by-step explanation:

We have to find the effect on the graph of the function $f(x)=2x$ when it is replaced by f(x- 3/5).

We already have an idea that rule for horizontal translation:

Given a function $f(x)$ , and a constant c > 0, the function $g(x) = f(x - a)$ represents a horizontal shift c units to the right from f(x). The function $h(x) = f(x + a)$ represents a horizontal shift c units to the left.

As 3/5 > 0, so the graph of the function will translate horizontally 3/5 units right.

Therefore, the graph of the function will translate horizontally 3/5 units right.

Keywords: exponential function, translation function, growth factor

Learn more about exponential function and growth factor form brainly.com/question/10147339

#learnwithBrainly

6 0

3 years ago

HELP ASAP PLEASEEEEEEEEEE

Andrew [12]

Given the recursive formula, each terms is five time the previous one.

This means that:

$f(6)$ is 5 times $f(5)$ , which means $f(6)=5f(5)$
in turn, $f(5)$ is 5 times $f(4)$ , so we have $f(5)=5f(4)$ . This means that $f(6)=5f(5)=5\cdot 5f(4) = 25f(4)$
Finally, $f(4)=5f(3)$ So, substituting this back gives

$f(6)=25f(4)=25\cdot 5f(3)=125f(3)$

In general, since you have $f(n)=5f(n-1)$ , each time you compute a new term you multiply by a factor of 5, so if $m=n+k$ , you have

$f(m)=5^kf(n)$

4 0

2 years ago

1+ 3z= 40 what’s the answer to this problem I’m confused???

stepan [7]

Answer:

Step-by-step explanation:

subtract 1 on both sides

then divide by 3

to get 13

8 0

3 years ago

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Half of Hillary’s friend, Jamiz’s fourth grade class is female. Including Jamiz, there are 14 girls in the class. How many stude

Yuri [45]

Including Jamiz, there are 14 girls in the class. If this if half of the total number of pupils (as half are girls, the other half being boys) the total number of students is 14 × 2 = 28 students

3 0

2 years ago