Question

Jane is saving to buy a cell phone. She is given a $100 gift to start and saves me

$35 a month from her allowance. So after 1 month, Jane has saved $135.
Does it make sense to represent the relationship between the amount saved
and the number of months with one constant rate? Why or why not? Explain
your answer.

Answer 1

See explanation

Explanation:

Jane is given a $100 gift to start and saves $35 a month from her allowance.

• After 1 month, Jane has saved
  `\$100+\$35=\$135;`
• After 2 months, Jane has saved
  `\$100+2\cdot \$35=\$170;`
• After three months, Jane has saved
  `\$100+3\cdot \$35=\$205;`
• and so on

In general, after x months Jane has saved

`\$100+x\cdot \$35=\$(100+35x).`

This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.