Wes has been tracking the population of a town. the population was 3,460 last year and has been increasing by 1.35 times each year. how can wes develop a function to model this? a. f(x) = 3460(1.35)x where 1.35 is the rate of growth. b. f(x) = (3460 ⋅ 1.35)x where 1.35 is the rate of growth. c. f(x) = 1.35(3460)x where 3460 is the rate of growth. d. f(x) = 3460(x)1.35 where 3460 is the rate of growth.

The function is where 1.35 is the rate of growth.

Step-by-step explanation:

We know that the population was 3,460 last year and has been increasing by 1.35 times each year.

This is an example of an Exponential Growth:

Exponential growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

So we have a generally useful formula:

where

a = Initial value

b = Rate of growth

We know the initial value a = 3,460 and b = 1.35. Therefore the function to model is where 1.35 is the rate of growth.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."