Question

The population of Thomasville was 2,460 in 2006, and is growing at an annual rate of 3.5%. This can be modeled by the exponential function f(x) = 2460(1.035) ^x.
How does the function change over the interval from x=2 to x=3?
A. f(x) increases by 3.5%
B. f(x) decreases by 3.5%
C. f(x) increases by a factor of 2460
D. f(x) decreases by a factor of 2460
​

Answer 1

Answer:

A. f(x) increases by 3.5%

Step-by-step explanation:

Given:

City of Thomasville.

Population in 2006, $P_o$ = 2460

Exponential function, f(x) = 2460(1.035) ^x    ...equivalent to $P=P_o(1+r)^t$

Function change at x = 2, 3

According to the question:

Plugging the values of x= 2 and x=3 we have to find the population at different x.

So,

At x= 2                                      At x=3

⇒ $P_2=P_o(1+r)^t$                        ⇒ $P_3=P_o(1+r)^t$

⇒ $P_2=2460(1.035)^x$                     ⇒ $P_3=2460(1.035)^x$

⇒ $P_2=2460(1.035)^2$                     ⇒ $P_3=2460(1.035)^3$

⇒ $P_2=2622.4$                               ⇒ $P_3=2707.7$

Percent change :

⇒ $\triangle \% =\frac{Final\ value -Initial\ value}{Initial\ value} \times 100$

⇒ $\triangle \% = \frac{(P_3-P_2)}{P_2} \times 100$

⇒ $\triangle \% = \frac{(2707.7-2622.4)}{2622.4} \times 100$

⇒ $\triangle \% = 3.5$

So,

The function f(x) increases by 3.5% option A is the right choice.