QuestionCamden's starting salary is \ $43000, increasing \$2000 each year. What will his salary be after 7 years and after$ t$ years?

Studdy Solution

STEP 1

Assumptions1. The initial annual salary is $43,000. The annual salary raise is$ ,0003. The salary raise is given at the end of each year4. The raise is added to the previous year's salary to form the new salary for the next year

STEP 2

First, we need to find the formula for the salary after $t$ years. Since the salary increases by a constant amount each year, we can use the formula for an arithmetic sequence.
$Salary_t = Initial\, salary + (t-1) \\times Annual\, raise$

STEP 3

Now, plug in the given values for the initial salary and annual raise to calculate the salary after7 years.
$Salary7 = \$43,000 + (7-1) \\times \$2,000$

STEP 4

implify the expression.
$Salary7 = \$43,000 +6 \\times \$2,000$

STEP 5

Calculate the salary after7 years.
$Salary7 = \$43,000 + \$12,000 = \$55,000$ Camden would make $55,000 as a salary after7 years working for the company.

STEP 6

Now, let's find the general formula for the salary after $t$ years. We can use the same formula as in2.
$Salary_t = \$43,000 + (t-1) \\times \$2,000$ This is the formula for Camden's salary after $t$ years working for the company.

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QuestionCamden's starting salary is \ $43000, increasing \$2000 each year. What will his salary be after 7 years and after$ t$ years?

Studdy Solution

STEP 1

Assumptions1. The initial annual salary is $43,000. The annual salary raise is$ ,0003. The salary raise is given at the end of each year4. The raise is added to the previous year's salary to form the new salary for the next year

STEP 2

First, we need to find the formula for the salary after $t$ years. Since the salary increases by a constant amount each year, we can use the formula for an arithmetic sequence.
$Salary_t = Initial\, salary + (t-1) \\times Annual\, raise$

STEP 3

Now, plug in the given values for the initial salary and annual raise to calculate the salary after7 years.
$Salary7 = \$43,000 + (7-1) \\times \$2,000$

STEP 4

implify the expression.
$Salary7 = \$43,000 +6 \\times \$2,000$

STEP 5

Calculate the salary after7 years.
$Salary7 = \$43,000 + \$12,000 = \$55,000$ Camden would make $55,000 as a salary after7 years working for the company.

STEP 6

Now, let's find the general formula for the salary after $t$ years. We can use the same formula as in2.
$Salary_t = \$43,000 + (t-1) \\times \$2,000$ This is the formula for Camden's salary after $t$ years working for the company.

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QuestionCamden's starting salary is \43000,increasing$2000eachyear.Whatwillhissalarybeafter7yearsandafter43000, increasing \$2000 each year. What will his salary be after 7 years and after 43000,increasing$2000eachyear.Whatwillhissalarybeafter7yearsandaftert$ years?

Studdy Solution

STEP 1

Assumptions1. The initial annual salary is 43,000.Theannualsalaryraiseis43,000. The annual salary raise is 43,000.Theannualsalaryraiseis,0003. The salary raise is given at the end of each year4. The raise is added to the previous year's salary to form the new salary for the next year

STEP 2

STEP 3

Now, plug in the given values for the initial salary and annual raise to calculate the salary after7 years.Salary7=$43,000+(7−1)times$2,000Salary7 = \$43,000 + (7-1) \\times \$2,000Salary7=$43,000+(7−1)times$2,000

STEP 4

implify the expression.Salary7=$43,000+6times$2,000Salary7 = \$43,000 +6 \\times \$2,000Salary7=$43,000+6times$2,000

STEP 5

Calculate the salary after7 years.Salary7=$43,000+$12,000=$55,000Salary7 = \$43,000 + \$12,000 = \$55,000Salary7=$43,000+$12,000=$55,000Camden would make $55,000 as a salary after7 years working for the company.

STEP 6

Now, let's find the general formula for the salary after ttt years. We can use the same formula as in2.Salaryt=$43,000+(t−1)times$2,000Salary_t = \$43,000 + (t-1) \\times \$2,000Salaryt​=$43,000+(t−1)times$2,000This is the formula for Camden's salary after ttt years working for the company.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCamden's starting salary is \ $43000, increasing \$2000 each year. What will his salary be after 7 years and after$ t$ years?

Assumptions1. The initial annual salary is $43,000. The annual salary raise is$ ,0003. The salary raise is given at the end of each year4. The raise is added to the previous year's salary to form the new salary for the next year

Now, plug in the given values for the initial salary and annual raise to calculate the salary after7 years.
$Salary7 = \$43,000 + (7-1) \\times \$2,000$

implify the expression.
$Salary7 = \$43,000 +6 \\times \$2,000$

Calculate the salary after7 years.
$Salary7 = \$43,000 + \$12,000 = \$55,000$ Camden would make $55,000 as a salary after7 years working for the company.

Now, let's find the general formula for the salary after $t$ years. We can use the same formula as in2.
$Salary_t = \$43,000 + (t-1) \\times \$2,000$ This is the formula for Camden's salary after $t$ years working for the company.