Respuesta :
Answer:
[tex]N(d)=2e^{0.32d}[/tex]
Step-by-step explanation:
Because the growth rate is not constant (as it changes after 2007), then we must find an average rate to use the continue exponential growth function which is given by:
[tex]N(d)=N_{0}e^{rd}[/tex]
Where,
d: number of periods
N(d): total number of blogs in d periods (in millions).
[tex]N_{0}:[/tex]: total number of blogs on the initial period (in millions)
r: average growth rate (this is the one we must find)
With the given information we may consider that:
d=14 The reason for this is that between March 2004 to March 2011 there are 7 years with 14 periods of 6 months(2x7).
N=175 (millions)
[tex]N_{0}=2[/tex] (millions)
Therefore,
[tex]175=2e^{14r}[/tex]
We find r by solving the equation above:
[tex]\frac{175}{2}=e^{14r}[/tex]
[tex]Ln\frac{175}{2}=14r[/tex]
[tex]r=\frac{Ln(175/2)}{14}=0.32[/tex]
Therefore our formula is as it follows:
[tex]N(d)=2e^{0.32d}[/tex]
This is about Exponential decay functions.
N(t) = N₀[tex]e^{0.3194d}[/tex]
- The general formula to express exponential growth functions is given by;
N(t) = N₀[tex]e^{dr}[/tex]
Where;
N is the amount of blogs remaining after t years
N₀ is the initial amount of blogs
r is the growth rate
d is the number of doubling periods
- We are given;
N₀ = 2 million blogs
number of years is; 2011 - 2004 = 7 years.
Thus doubling periods is; d = 2 × 7 = 14
N(14) = 175 million
- Plugging in the relevant values, we have;
175 = 2[tex]e^{14r}[/tex]
divide both sides by 2 to get;
87.5 = [tex]e^{14r}[/tex]
In 87.5 = 14r
14r = 4.4716
r = 4.4716/14
r = 0.3194
Thus;
formula is; N(t) = N₀[tex]e^{0.3194d}[/tex]
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