Which graph best represents a decreasing function?

A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

erastovalidia [21]

Answer:

The average yearly salary of the architect is $62,000 and the lawyer is $100,000.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of an architect and a lawyer.

Let the average yearly salary of an architect be $x.$

So, the average yearly salary of the lawyer = $2x-24,000.$

Combined, architect and lawyer earn = $\$210,000.$

Now, to get the average salary of the architect and lawyer:

$x+(2x-24000)=210000$

$x+2x-24000=210000\\\\3x-24000=210000$

Adding both sides 24000 we get:

$3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.$

The average salary of architect = $62,000.

Now, to get the average salary of lawyer by substituting the value of $x$ :

$2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.$

The average salary of lawyer = $100,000.

Therefore, the average yearly salary of the architect is $62,000 and the lawyer is $100,000.

4 0

4 years ago

What's the reciprocal of 5?

olganol [36]

That would be 0.2

Hope this helps. :)

6 0

3 years ago

Kathy was building a bed for her dollhouse. She used her bed, which is 3 feet × 5 feet, as a guide. She scaled down the dimensio

andrew-mc [135]

I think the answer is D)

4 0

3 years ago

You want a soccer ball. It costs $10.00. Because everyone wants the item, the price goes up 6%. Find the new price

Vitek1552 [10]

X/10.00 = 6/100
So you would first do 6 times 10.00 which is 60.00 then divid by 100 then you will get your answer

4 0

3 years ago

Read 2 more answers

The function y = 58. 7(1. 03)^t gives a country’s population, y (in millions), where t is the number of years since January 1994

GREYUIT [131]

Answer:

Approximate population ≈ 74.36 million.

Step-by-step explanation:

The given problem involves modeling of an exponential growth or decay function of a population.

<h2>Definition:</h2>

Exponential growth ( relative growth ) occurs when a population grows or increases exponentially by the same factor, over the same amount of time.
Exponential decay occurs when a population decreases continuously by a constant factor, over the same amount of time.

We can model the exponential growth of a population using the following Exponential Growth Model:

⇒ $\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$

Where:

P( t ) = population after "t" years
P₀ = initial population
r = relative growth rate; positive "r" value means that the population is increasing; negative "r" value implies that the population is decreasing.
t = time (typically in years)

<h2>Solution:</h2>

Based from the given equation, $\displaystyle\mathsf{y\:=\:58.7(1.03)^t }$ , we can infer that:

⇒ $\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$ or $\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }$

Where:

P( t ) or y = population after "t" years
P₀ = initial population = 58.7
r = relative growth rate = 0.03 or 3% = the population is increasing (exponential growth).
t = time (typically in years) = 8 years (difference between January 2002 and January 1994).

Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :

$\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }$

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }$

Step 2: Follow the order of operations, addition inside the parenthesis:

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }$

Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):

⇒ $\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }$

Step 4: Follow the order of operations, multiplying 58.7 (P₀) into the parenthesis:

⇒ $\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}$

<h2>Final Answer:</h2>

Therefore, the approximate population of the country in January 2002 is 74.36 million.

<h3>________________________</h3><h3>Keywords:</h3>

Exponential functions

Exponential growth

Exponential decay

Exponential growth model

____________________________

Learn more about exponential functions here:

brainly.com/question/25802424

7 0

3 years ago