Question

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

click twice to plot each line. click a line to delete it.

(graph with total in savings (dollars) on y - axis and number of weeks on x - axis)

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 \( S(t) = 90 + 10t \).

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 \( I(t) = 50 + 20t \).

Step3: Calculate Savannah's savings after 6 weeks

Substitute \( t = 6 \) into \( S(t) \): \( S(6) = 90 + 10\times6 = 90 + 60 = 150 \).

Step4: Calculate Isaac's savings after 6 weeks

Substitute \( t = 6 \) into \( I(t) \): \( I(6) = 50 + 20\times6 = 50 + 120 = 170 \).

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.