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

A. f(x) increases by 3.5%

Step-by-step explanation:

Given:

City of Thomasville.

Population in 2006, = 2460

Exponential function, f(x) = 2460(1.035) ^x    ...equivalent to

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

⇒                        ⇒

⇒                     ⇒

⇒                     ⇒

⇒                               ⇒

Percent change :

⇒

⇒

⇒

⇒

So,

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

55

step-by-step explanation:

you can use a^2+ b^2=c^2