Answer: She started with $160.
It will take 6 weeks before she has less than half of what she originally invested.
Step-by-step explanation:
If her money is decreasing in value by 11% each week, it means that the rate at which it is decreasing is exponential.
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the investment after t weeks.
t represents the number of weeks.
P represents the initial value of the investment.
r represents rate of depreciation.
From the information given,
A = $142.40
r = 11% = 11/100 = 0.11
t = 1
Therefore
142.40 = P(1 - 0.11)^1
142.40 = P(0.89)
P = 142.4/0.89
P = 160
For her to have half of what she invested originally, then
80 = 160(0.89)^t
80/160 = (0.89)^t
0.5 = (0.89)^t
Taking log of both sides to base 10
Log 0.5 = log0.89^t = tlog0.89
- 0.3010 = - 0.051t
t = - 0.3010/- 0.051
t = 5.9
Approximately 6 weeks
Answer: 20 oranges and 5 mangoes
Step-by-step explanation:
Define the following:
x = number of oranges
y = number of mangoes
Make the following system of equations:
x + y = 25
0.35x + 1.00y = 12.00
Solve for x:
y = 25 - x
⇒ 0.35x + 1.00(25 - x) = 12.00
⇒ 0.35x + 25 - x = 12.00
⇒ -0.65x = -13.00
⇒ x = 20
Solve for y:
20 + y = 25
y = 5
∴ 20 oranges and 5 mangoes were purchased.
