Respuesta :
Answer:
The correct estimate of the amount generated to the local economy is $3,333,333.[tex]\bar3[/tex]
Step-by-step explanation:
The amount the expected to be generated for the local economy = $3.3 million
The amount of salaries that will generate $3.3 million = $1 million
The percentage of the amount of the salaries and the subsequent earnings expected to be spent on the local community = 70%
Therefore, we have;
For a first amount of 1 million into the economy, the next amount to into the economy is 70/100 × 1 million = 700,000, then we have 70/100 × 700,000 and so on, which is a geometric sequence, with first term, a = $1 million, the common ratio, r = 70/100 = 0.7, the number of terms = Infinity = ∞
The sum of a geometric sequence to infinity is given as follows;
[tex]\sum\limits_{k = 0}^{\infty }a \cdot r^k = S_{\infty} = \dfrac{a}{1 - r}[/tex]
Substituting the known values gives;
[tex]\sum\limits_{k = 0}^{\infty }1,000,000 \times 0.7 ^k = \dfrac{1,000,000}{1 - 0.7}= 3,333,333.\bar 3[/tex]
Therefore, the correct estimate of the amount generated to the local economy by the $1 million salaries that will be paid = $3,333,333.[tex]\bar3[/tex].
