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MrRissso [65]
3 years ago
9

Ms Acosta received a job as a teacher with a starting salary of $34,000 according to her contract she will receive a 1.5% increa

se in her salary every year how much will mas Acosta earn in 7 years

Mathematics
1 answer:
Damm [24]3 years ago
4 0

Answer: In 7 years, Ms Acosta will earn $37,734.7

Step-by-step explanation:

From the information given, we find the increase using exponential growth formula

A= P(1+r)^t

Where p= the starting amount on the contract, given as $34000

r = rate, given at 1.5% = 1.5/100 = 0.015

t = time, given as 7years

Plug the values into the formula:

A = 34000(1 + 0.015) ^7

= 34000 (1.015)^7

34000 x 1.1098

A= $37,734.7

In 7 years, Ms Acosta will earn $37,734.7.

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Break apart ones to make a ten<br><br> 62 + 9 =
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Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
gladu [14]

Answer:

Vertical asymptote: x=3

Horizontal asymptote: f(x) =2

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

f (x) = -\dfrac{1 }{ x-3} +2

One root, x = 3.5

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5

One root, x = 3.5

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) \rightarrow \infty

For all, other values of x , f(x) is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is \frac{1}{x-3}.

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) \rightarrow \infty.

-\dfrac{1 }{ x-3} +2 \rightarrow \infty

It is possible only when

x-3=0\\\Rightarrow x=3

\therefore vertical asymptote: x=3

Horizontal Asymptote is the value of f(x) , where value of x \rightarrow \infty.

x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2

\therefore Horizontal asymptote: f(x) =2

Please refer to the graph of given function as shown in the attached image.

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3 years ago
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