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, y=〖b(1+r)〗^t, 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 exponential model is $y=382627(1.0278)^t$.

Step-by-step explanation:

The exponential formula is

$y=b(1+r)^t$

Where b is initial population, r is growth rate and t is time (in years).

The population of the Tallahassee metropolitan area was 382,627 at the end of 2017. The growth rate is 2.78%.

$y=382627(1+0.0278)^t$

$y=382627(1.0278)^t$

Graph of the equation is shown below. The x-axis represents the number of years after 2017 and y-axis represents the total population.

Difference between 2025 and 2017 is 8 years. Put t=8

$y=382627(1.0278)^8$

$y=382627(1.0278)^8$

$y=476479.828188\approx 476479$

Therefore the projected population in 2025 is 476479.

Answer 2

The graph is shown in the attachment.

Further explanation

Function is a relation which each member of the domain is mapped onto exactly one member of the codomain.

There are many types of functions in mathematics such as :

• Linear Function → f(x) = ax + b

• Quadratic Function → f(x) = ax² + bx + c
• Trigonometric Function → f(x) = sin x or f(x) = cos x or f(x) = tan x
• Logarithmic function → f(x) = ln x
• Polynomial function → f(x) = axⁿ + bxⁿ⁻¹ + ...

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If function f : x → y , then inverse function f⁻¹ : y → x

Let us now tackle the problem!

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A graph of exponential function has the general form:

$\boxed {f(x) = a (b)^x}$

Given:

$y = b ( 1 + r )^t$

If the population of the Tallahassee metropolitan area was 382,627 at the end of 2017 with a growth rate of 2.78% , then :

b = 382,627

r = 2.78% = 0,0278

$y = b ( 1 + r )^t$

$y = 382,627 ( 1 + 0,0278 )^t$

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The y-intercept is found when t = 0 , then:

$y = 382,627 ( 1 + 0,0278 )^t$

$y = 382,627 ( 1 + 0,0278 )^0$

$y = 382,627$

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The population in 2025 will be :

$y = 382,627 ( 1 + 0,0278 )^t$

$y = 382,627 ( 1 + 0,0278 )^{ 2025 - 2017 }$

$y = 382,627 ( 1 + 0,0278 )^{ 8 }$

$y = 382,627 ( 1,0278 )^{ 8 }$

$y \approx 476480$

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Learn more

• Inverse of Function : https://brainly.com/question/9289171
• Rate of Change : https://brainly.com/question/11919986
• Graph of Function : https://brainly.com/question/7829758

Answer details

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic