G(x)=-(x+1)(r-1)(-4) In standard form?? Please help!
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Answer:
Approximate population ≈ 74.36 million.
Step-by-step explanation:
The given problem involves modeling of an exponential growth or decay function of a population.
<h2>Definition:</h2>- Exponential growth ( <em>relative growth </em>) occurs when a population grows or <u><em>increases</em></u> exponentially by the same factor, over the same amount of time.
- Exponential decay occurs when a population <u><em>decreases</em></u> continuously by a <em>constant factor</em>, over the same amount of time.
We can model the exponential growth of a population using the following Exponential Growth Model:
- ⇒
Where:
- P( <em>t</em> ) = population after "<em>t</em><em>" </em>years
- <em>P₀ </em>= initial population
- <em>r</em> = relative growth rate; <u><em>positive "r" value</em></u><em> </em>means that the population is increasing; <u><em>negative "r" value</em></u> implies that the population is decreasing.
- <em>t </em>= time (typically in <em>years</em>)
Based from the given equation, , we can infer that:
⇒ or
Where:
- P( <em>t</em> ) or <em>y</em> = population after "<em>t" </em>years
- <em>P₀ </em>= initial population = 58.7
- <em>r</em> = relative growth rate = 0.03 or 3% = the population is <em>increasing</em> (exponential growth).
- <em>t </em>= time (typically in <em>years</em>) = 8 years (difference between January 2002 and January 1994).
Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :
⇒
Step 2: Follow the order of operations, <u><em>addition</em></u> inside the parenthesis:
⇒
Step 3: Follow the order of operations, applying the <u><em>exponent</em></u> into the parenthesis (do not round off the digits inside the parenthesis):
⇒
Step 4: Follow the order of operations, <u><em>multiplying</em></u> 58.7 (<em>P₀</em>) into the parenthesis:
⇒
Therefore, the approximate population of the country in January 2002 is 74.36 million.
<h3>________________________</h3><h3><em>Keywords:</em></h3>Exponential functions
Exponential growth
Exponential decay
Exponential growth model
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Learn more about exponential functions here: