started?(1 point)
Manuel de Mier y Terán
Anastasio Bustamante
Antonio López de Santa Anna
Lucas Alamán y Escalada
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The president of Mexico when the Law of April 6, 1830, was passed was Anastasio Bustamante. He also served during the start of the civil war in Mexico, known as the Texas Revolution, which began in 1835. Therefore, the correct answer is:
Anastasio Bustamante
To convert the given exponential growth formula from a decade-based increment to a 2-year increment, you need to determine the growth rate over 2 years.
The original formula is:
\[ p(d) = 1,000,000(1 + 0.15)^d \]
Where \( d \) is the number of decades. Since a decade consists of 10 years, we first need to find the equivalent growth factor for 2 years.
The growth factor for 10 years (1 decade) is \( 1 + 0.15 = 1.15 \).
To find the growth factor for 2 years, you can take the 10-year growth factor and raise it to the power of \(\frac{2}{10}\) (which is the fraction of the decade that 2 years represents):
\[ \text{Growth factor for 2 years} = (1.15)^{\frac{2}{10}} = (1.15)^{0.2} \]
Now we need to calculate this value: \[ 1.15^{0.2} \approx 1.02899 \text{ (or roughly 1.029)} \]
Now, we can express the population growth based on 2-year increments. The number of 2-year increments in \( d \) decades is \( 5d \) (since there are 5 sets of 2 years in a decade).
Thus, the population formula that incorporates 2-year increments becomes:
\[ p(n) = 1,000,000(1.15^{0.2})^n \]
Where \( n \) is the number of 2-year increments. Simplifying gives us:
\[ p(n) = 1,000,000 (1.029)^n \]
This formula can now be used to predict the city's population growth every 2 years based on the initial population of 1,000,000 and the growth factor for 2 years.
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