Answer: The true statement is,
The rate at which the balance of Account A grows is greater than the rate at which the balance of Account B grows.
Step-by-step explanation:
Given inequalities that represents the amount in two different account,
Account A: y ≥ 1.13x+1000,
Account B: y ≥ 1.08x+1000,
Since, the amount of an investment represents by the linear equation,
y = ax + b
Where,
b = invested amount,
a = amount of interest per period,
x = number of periods,
Since, related equation of inequality y ≥ 1.13x+1000,
y = 1.13x+1000,
i.e invested amount = 1000, interest per year = 1.13,
Similarly, related equation of inequality y≥1.08x+1000,
y = 1.08x+1000,
i.e invested amount = 1000, interest per year = 1.08,
⇒ Sally initially invests same money into Account A than Account B
⇒ Sally invests a total of $2000 into the two accounts.
Now, 1.08 < 1.13
∵ interest ∝ rate × time,
Hence, the rate at which the balance of Account A grows is greater than the rate at which the balance of Account B grows.
