Question

(04.05 MC)

Answer 1

Answer:

A) increasing by 9% each year

B) Account B

Step-by-step explanation:

$f(x)=1264(1.09)^x$

Part A

The amount of money in account A is increasing by 9% each year.

General form of an exponential function:  $f(x)=ab^x$

$a$ is the initial value, $b$ is the growth factor and $x$ is time.

• If b < 1 then the function is decreasing
• If b > 1 then the function is increasing

As b = 1.09 > 1 then the function is increasing

$b$ is the decimal form of percentage change.

Therefore, for b > 1, percentage increase = b - 1

for b < 1, percentage decrease = 1 - b

So as b = 1.09 > 1, percentage increase = 1.09 - 1 = 0.09 = 9%

Part B

From inspection, the amount in account B is increasing exponentially.

Therefore, we can use $y=ab^x$

To determine the growth factor $b$, divide one value of g(r) by its previous value:

$\implies b=\dfrac{1512.50}{1375}=\dfrac{11}{10}=1.1$

$\implies g(r)=a(1.1)^r$

To determine $a$, input a pair of values (r, g(r)) into the equation and solve:

$\implies 1375=a(1.1)^1$

$\implies a=\dfrac{1375}{1.1}=1250$

Therefore, the equation for account B:  $g(r)=1250(1.1)^r$

Comparing the growth factor $b$ of both equations, account B recorded a greater percentage change in amount of money over the previous year since 1.1 > 1.09