Question

at the beginning of the year, savannah had $90 in savings and saved an additional $10 each week thereafter. isaac started the year with $50 and saved $20 every week. let ( s ) represent the amount of money savannah has saved ( t ) weeks after the beginning of the year and let ( i ) represent the amount of money isaac has saved ( t ) weeks after the beginning of the year. graph each function and determine the who has more money saved after 6 weeks.

(graph: y - axis labeled total in savings (dollars) from 0 to 200, t - axis labeled number of weeks from 0 to 20. instruction: click twice to plot each line. click a line to delete it.)

Explanation:

Step1: Define Savannah's savings function

Savannah starts with $90 and saves $10 per week. So the function for her savings \( S \) after \( t \) weeks is \( S = 90 + 10t \).

Step2: Define Isaac's savings function

Isaac starts with $50 and saves $20 per week. So the function for his savings \( I \) after \( t \) weeks is \( I = 50 + 20t \).

Step3: Calculate savings after 6 weeks for Savannah

Substitute \( t = 6 \) into Savannah's function: \( S = 90 + 10(6) = 90 + 60 = 150 \).

Step4: Calculate savings after 6 weeks for Isaac

Substitute \( t = 6 \) into Isaac's function: \( I = 50 + 20(6) = 50 + 120 = 170 \).

Step5: Compare the two amounts

Since \( 170 > 150 \), Isaac has more money saved after 6 weeks.

Answer:

Isaac has more money saved after 6 weeks. Savannah has $150 and Isaac has $170.