question 5\nthe equations that represent the balance in three different savings accounts x years after…

question 5\nthe equations that represent the balance in three different savings accounts x years after 2012,\n$a = 900(1.05)^x$\n$b = 1100(1.038)^x$\n$c = 5000(0.85)^x$\nwhich of the following statements are true? check all that apply.\naccount c had the largest balance in the year 2012.\nthe balance of account c is decreasing at a rate of 85% per year.\naccount a is growing faster than account b.\nthe balance of account a is growing at a rate of 5% per year.

question 5\nthe equations that represent the balance in three different savings accounts x years after 2012,\n$a = 900(1.05)^x$\n$b = 1100(1.038)^x$\n$c = 5000(0.85)^x$\nwhich of the following statements are true? check all that apply.\naccount c had the largest balance in the year 2012.\nthe balance of account c is decreasing at a rate of 85% per year.\naccount a is growing faster than account b.\nthe balance of account a is growing at a rate of 5% per year.

Answer

Explanation:

Step1: Find initial balance in 2012 (x = 0)

When (x = 0), for account A: (A=900(1.05)^0=900); for account B: (B = 1100(1.038)^0=1100); for account C: (C=5000(0.85)^0 = 5000). So account C had the largest balance in 2012.

Step2: Analyze the rate of change of account C

The general form of an exponential - decay function is (y = a(1 - r)^x), where (r) is the rate of decay. For (C = 5000(0.85)^x), the rate of decay is (1-0.85=0.15) or 15% per year, not 85% per year.

Step3: Compare the growth rates of account A and B

The growth rate of account A is (1.05 - 1=0.05) or 5% per year. The growth rate of account B is (1.038 - 1 = 0.038) or 3.8% per year. So account A is growing faster than account B.

Step4: Identify the growth rate of account A

For (A = 900(1.05)^x), the growth rate is (1.05-1 = 0.05) or 5% per year.

Answer:

Account C had the largest balance in the year 2012. Account A is growing faster than account B. The balance of Account A is growing at a rate of 5% per year.