Answer:
Left: The substance is decreasing by 1/2 every 12 years
Right: The substance is decreasing by 5.61% each year
Step-by-step explanation:
exponential decay
A = P(1-r)ᵇⁿ, where A is the final amount, P is the initial amount, r is the rate decreased each time period, b is the number of years, and n is the number of times compounded each year
let's write each formula in terms of this
left:
f(t) = 600(1/2)^(t/12)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1/2 -> r = 1/2
t/12 = bn -> b = number of years = t, so bn = b/12 -> n = 1/12. Thus, it is compounded 1/12 times each year, so it is compounded every t*12 = 12 years. If it was compounded each month, it would be compounded 12 times a year
Thus, this is decreasing by a rate of 1/2 each 12 years
right:
f(t) = 600(1-0.0561)^(t)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1 - 0.0561 -> r = 0.0561 = 5.61%
t = bn -> b = number of years = t, so bn = b -> n = 1. Thus, it is compounded annually (1 time each year)
Thus, this is decreasing by a rate of 5.61% each year
The answer will be 0.026666666666 or just put a little sgwigly line ~ kind of like that to show that the last number will go on and in forever hope this helps!! Ask me any other questions if you have any.
Answer:
-9/3 or -3
Step-by-step explanation:
Answer:
$40
Step-by-step explanation:
x is the original price of the gift
(10% of x) is the value of the discount
(10% of x) = 10/100 . x = 0.1 x
0.1 x is the value of the discount
x - (10% of x) is what was paid, after the discount
x - 0.1 x = 0.9 x
0.9 x is what was paid
4 children paid $9/each
4 times $9 = $36
$36 is the total amount that was paid by the children
$36 = 0.9 x
$36 / 0.9 = x
x = $36 / 0.9 = 360 / 9
x = 40
;-)
Answer:
26
Step-by-step explanation:
→ Utilise Pythagoras theorem
a² + b² = c²
→ Substitute in the values
10² + 24² = c²
→ Simplify
100 + 576 = c²
→ Simplify further
676 = c²
→ Square root both sides to isolate c
26 = c
