Mathematics: Acountry s population in 1994 was 182 million. in 2002 it was 186 million. estimate the population in 2004 using the exponential growth formula. round your answer to the nearest million. p=ae^kt

Acountry s population in 1994 was 182 million. - id199418222188798, chanel2371

Ответ:

alen919

02.01.2022

$\bf =ae^{kt}\qquad 
\begin{cases}
1994\impliedby \textit{year 0, starting point}\\
t=0\qquad P=182
\end{cases}\implies 182=ae^{k0}
\\\\\\
182=a\cdot e^0\implies 182=a\cdot 1\implies 182=a
\\\\\\
thus\qquad P=182e^{kt}\\\\
-------------------------------\\\\$

$\bf P=182e^{kt}\qquad 
\begin{cases}
2002\impliedby \textit{8 years later}\\
t=8\qquad P=186
\end{cases}\implies 186=182e^{k8}
\\\\\\
\cfrac{186}{182}=e^{8k}\implies ln\left( \frac{93}{91} \right)=ln(e^{8k})\implies ln\left( \frac{93}{91} \right)=8k
\\\\\\
\cfrac{ln\left( \frac{93}{91} \right)}{8}=k\implies 0.0027\approx k\implies \boxed{P=182e^{0.0027t}}$

what's the population in 2004? well, from 1994 to 2004 is 10 years later, so t = 10

plug that in, to get P for 2004

0,0(0 оценок)

Acountry's population in 1994 was 182 million. in 2002 it was 186 million. estimate the population in 2004 using the exponential growth formula. round your answer to the nearest million. p=ae^kt

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question