question 39\nthe balance of an account t years after it is opened can be modeled by $a(t)=600(1.04)^t$. what…

question 39\nthe balance of an account t years after it is opened can be modeled by $a(t)=600(1.04)^t$. what is the average rate of change in the balance from $t = 3$ to $t = 10$?\na) $7.00 per year\nb) $28.81 per year\nc) $30.46 per year\nd) $21.32 per year

question 39\nthe balance of an account t years after it is opened can be modeled by $a(t)=600(1.04)^t$. what is the average rate of change in the balance from $t = 3$ to $t = 10$?\na) $7.00 per year\nb) $28.81 per year\nc) $30.46 per year\nd) $21.32 per year

Answer

Answer:

C. $30.46 per year

Explanation:

Step1: Calculate $A(3)$

$A(3)=600\times(1.04)^{3}=600\times1.124864 = 674.9184$

Step2: Calculate $A(10)$

$A(10)=600\times(1.04)^{10}=600\times1.4802442849 = 888.14657094$

Step3: Use average - rate - of - change formula

The average rate of change of a function $y = A(t)$ from $t=a$ to $t = b$ is $\frac{A(b)-A(a)}{b - a}$. Here, $a = 3$, $b = 10$. So the average rate of change is $\frac{A(10)-A(3)}{10 - 3}=\frac{888.14657094 - 674.9184}{7}=\frac{213.22817094}{7}\approx30.46$