Which expression can be used to find the salary, in thousands, for the second year? Select all that apply.
$400+(0.05) 400$
$400+(1.05) 400$
400(1.05)
$(0.05) 400+(.05) 400$
Answer (2)
The problem involves calculating the salary for the second year given an initial salary of 400 thousand and a 5% annual increase.
The salary for the second year can be expressed as the initial salary plus the 5% increase: 400 + 0.05 × 400 .
Factoring out 400 , the salary for the second year can also be expressed as: 400 ( 1 + 0.05 ) = 400 ( 1.05 ) .
Therefore, the correct expressions are 400 + ( 0.05 ) × 400 and 400 ( 1.05 ) . The final answer is 400 + ( 0.05 ) × 400 , 400 ( 1.05 )
Explanation
Understanding the Problem Let's analyze the problem. We are given an initial salary of 400 thousand and an annual increase of 5% . We want to find the expression(s) that represent the salary for the second year.
Calculating the Second Year's Salary The salary for the first year is 400 thousand. The salary for the second year is the first year's salary plus a 5% increase.
Expression 1 We can express the second year's salary as: 400 + 0.05 × 400
This represents the initial salary plus the 5% increase.
Expression 2 We can also factor out 400 from the expression: 400 ( 1 + 0.05 ) = 400 ( 1.05 )
This is another way to represent the second year's salary.
Evaluating the Expressions Let's evaluate the given expressions:
400 + ( 0.05 ) × 400 = 400 + 20 = 420
400 + ( 1.05 ) × 400 = 400 + 420 = 820
400 ( 1.05 ) = 420
( 0.05 ) × 400 + ( 0.05 ) × 400 = 20 + 20 = 40
Identifying Correct Expressions From the calculations, we can see that the expressions 400 + ( 0.05 ) × 400 and 400 ( 1.05 ) both correctly represent the salary for the second year, which is 420 thousand.
Final Answer Therefore, the expressions that can be used to find the salary, in thousands, for the second year are:
400 + ( 0.05 ) × 400 400 ( 1.05 )
Examples
Understanding percentage increases is crucial in many real-life situations. For example, when calculating salary increases, investment growth, or even price markups in retail, the same principles apply. If you invest 5000 in a stock that grows by 8% annually, you can calculate the value of your investment after one year using the same formula: $5000 \times (1 + 0.08) = 5400 . This fundamental concept helps in making informed financial decisions.
The expressions that correctly calculate the salary for the second year are 400 + ( 0.05 ) ⋅ 400 and 400 ( 1.05 ) , both resulting in a total of 420 thousand. The expression 400 + ( 1.05 ) ⋅ 400 results in an incorrect total of 820 thousand, and ( 0.05 ) ⋅ 400 + ( 0.05 ) ⋅ 400 gives 40 thousand, which is also incorrect. Thus, the correct answers are the first and third expressions.
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