De shawn is in his fifth year of employment as a patrol officer for the metro police. his salary for his first year of employment was $47,000. each year after the first, his salary increased by 4% of his salary the previous year.

to obtain the sum of deshawn's salaries for the first five years of service, we can use f(x)=47,000(1.04)^x , where x gives the salary x years after his first year.

salary after 5 years = f(0) + f(1) + f(2) + f(3) + f(4) +f(5) = $245,567.

if deshawn continues his employment at the same rate of increase in yearly salary, for which year will the sum of his salaries first exceed $1,000,000?

(the answer should be 16, but i don't know how to get it.)

After 16 years De Shawn salary will exceed $1000000.

Step-by-step explanation:

First year salary of De Shawn as a petrol officer was $47000.

Each year increase in his salary was 4%.

Second year his salary will be = ($47000 + 4% of $47000) = $48880

Third year the salary will be = ($48880 + 4% of 48880) = $50835.20

Then every year his salary will be $47000, $48880, $50835...........

The sequence formed will be a geometric sequence having common ratio 'r' = (1+0.04) = 1.04

First term of this sequence = $47000

Since sum of a geometric sequence is represented by

We have to find the value of x (Number of years) after which the salary will be = $1000000

21.2766×0.04 + 1 =

1.851 =

By taking log on both the sides

log(1.851) =

0.2764 = xlog(1.04)

x =

x = 16.26 years

Therefore, after 16 year De Shawn's salary will exceed $1000000.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

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step-by-step explanation:

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