the cost of mailing a first-class letter is $0.46 for the first ounce and $0.20 for each additional ounce or…

the cost of mailing a first-class letter is $0.46 for the first ounce and $0.20 for each additional ounce or portion of an ounce. the letter y represents the total cost for mailing a letter that weighs x ounces. which type of function model would be appropriate for this situation?\nabsolute value function linear function step function square root function

the cost of mailing a first-class letter is $0.46 for the first ounce and $0.20 for each additional ounce or portion of an ounce. the letter y represents the total cost for mailing a letter that weighs x ounces. which type of function model would be appropriate for this situation?\nabsolute value function linear function step function square root function

Answer

Explanation:

Step1: Analyze the Cost Structure

The cost for the first ounce is $0.46. For each additional ounce or portion of an ounce, it's $0.20. So, if the weight is between ( n ) and ( n + 1 ) ounces (where ( n ) is a non - negative integer, ( n\geq1 )), the cost will be ( 0.46+0.20n ). For example, if the weight is 1.1 ounces, it's still charged as 2 ounces (1 first ounce + 1 additional ounce), cost is ( 0.46 + 0.20\times1=0.66 ). If it's 2 ounces, cost is ( 0.46+0.20\times1 = 0.66 ), and if it's 2.1 ounces, cost is ( 0.46+0.20\times2 = 0.86 ).

Step2: Identify the Function Type

  • Absolute value function: Has a V - shape and is used to represent distances or values with a magnitude - related property. This does not match the cost - weight relationship here.
  • Linear function: A linear function has the form ( y = mx + b ) where the rate of change ( m ) is constant and the function is continuous. But in our case, the cost jumps at each integer value of weight (e.g., from 1.9 ounces to 2.0 ounces, the cost increases by $0.20), so it's not a linear function.
  • Step function: A step function is a piece - wise constant function where the function value changes at distinct points (in this case, at each integer weight value) and remains constant over intervals. This matches our cost - weight relationship as the cost remains the same for any weight in the interval ( (n,n + 1] ) (for ( n\geq0 ), with ( n = 0 ) corresponding to the first ounce) and then jumps at ( n+1 ).
  • Square root function: Has a curve that starts at the origin (or a non - negative point) and increases slowly. It has no relation to the step - like cost structure here.

Answer:

step function