Question

question 1-8 luis has saved $6. he doubles the amount he has saved each week. does the situation represent an exponential function? yes no does the function have a constant difference or a constant ratio? difference ratio

Explanation:

Step1: Analyze the situation

Luis starts with $6 and doubles the amount each week. Let's list the amounts over weeks:

• Week 0: $6
• Week 1: $6\times2 = $12
• Week 2: $12\times2 = $24
• Week 3: $24\times2 = $48

Step2: Check for exponential function

An exponential function has a constant ratio between consecutive terms. Let's check the ratios:

• Ratio of Week 1 to Week 0: $\frac{12}{6}=2$
• Ratio of Week 2 to Week 1: $\frac{24}{12}=2$
• Ratio of Week 3 to Week 2: $\frac{48}{24}=2$

The ratio is constant (2), so it represents an exponential function.

Step3: Check constant difference or ratio

For constant difference, we check the differences:

• Difference between Week 1 and Week 0: $12 - 6 = 6$
• Difference between Week 2 and Week 1: $24 - 12 = 12$
• Difference between Week 3 and Week 2: $48 - 24 = 24$

Differences are not constant. But the ratio is constant (as seen in Step 2).

Answer:

• Does the situation represent an exponential function? $\boldsymbol{\text{yes}}$
• Does the function have a constant difference or a constant ratio? $\boldsymbol{\text{ratio}}$