Question

The population of the Tallahassee metropolitan area was 382,627 at the end of 2017 with a growth rate of 2.78%. Using the exponential growth formula, sketch the graph that represents the situation.

Label the axes, y-intercept and the point that represents the projected population in 2025.

Answer 1

Answer: The graph is represented below.

Explanation:

Here, the population of the Tallahassee metropolitan area was 382,627 at the end of 2017 with a growth rate of 2.78%.

Therefore, Initial population, P = 382,627

Annual Rate of growth, r= 2.78 %

⇒ After x years the population will be,

`f(x)=382627(1+2.78/100)^x`

`f(x)= 382627(1+0.0278)^x`

`f(x)= 382627(1.0278)^x`

Where 1.027 is the growth factor and y-intercept= (0,382627)

And, The population in 2025, x=8

`f(8)=382627(1.0278)^8`=476479.828188≈476480 (approx)

Therefore point that represents projected population in 2025 is ( 8, 476479.828188)