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:
[tex]y = C_{o}\cdot (1+ r)^{x}[/tex] (1)
Where:
[tex]C_{o}[/tex] - Initial amount, measured in monetary units.
[tex]r[/tex] - Rate, dimensionless. (The progression is increasing when [tex]r > 0[/tex], and decreasing when [tex]-1 < r < 0[/tex])
[tex]x[/tex] - Time, measured in months.
[tex]y[/tex] - Profit, measured in monetary units.
Given that [tex]y = 150,210\cdot (0.82)^{x}[/tex], we calculated the rate below:
[tex]1+r = 0.82[/tex]
[tex]r = 0.82-1[/tex]
[tex]r = -0.18[/tex]
The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.
b) If we know that [tex]x = 7[/tex], then the expected amount for Antonio in 7 months from now is:
[tex]y = 150,210\cdot (0.82)^{7}[/tex]
[tex]y = 37445.17[/tex]
Antonio is expected to make a profit of 37445.17 in 7 months from now.
