Answer:
a) The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.
b) Antonio is expected to make a profit of 37445.17 in 7 months from now.
Step-by-step explanation:
a) The equation described on statement represents a geometrical progression, which is defined as:
(1)
Where:
- Initial amount, measured in monetary units.
- Rate, dimensionless. (The progression is increasing when
, and decreasing when
)
- Time, measured in months.
- Profit, measured in monetary units.
Given that
, we calculated the rate below:
![1+r = 0.82](https://tex.z-dn.net/?f=1%2Br%20%3D%200.82)
![r = 0.82-1](https://tex.z-dn.net/?f=r%20%3D%200.82-1)
The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.
b) If we know that
, then the expected amount for Antonio in 7 months from now is:
![y = 150,210\cdot (0.82)^{7}](https://tex.z-dn.net/?f=y%20%3D%20150%2C210%5Ccdot%20%280.82%29%5E%7B7%7D)
Antonio is expected to make a profit of 37445.17 in 7 months from now.