Answer:
151.4863 years
Explanation:
Half life, t1/2 = 100 years
Initial concentration,[A]o = 100%
Final concentration, [A] = 35% (after 65% have been decayed)
Time = ?
Half life for a first Order reaction is given as;
t1/2 = ln (2) / k
k = ln(2) / 100
k = 0.00693y-1
The integral rate law for first order reactions is given as;
ln[A] = ln[A]o − kt
kt = ln[A]o - ln[A]
t = ( ln[A]o - ln[A]) / k
t = [ln(100) - ln(35)] /0.00693
t = 1.0498 / 0.00693
t = 151.4863 years
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Answer:
FV = $3506.112
Interest = $506.112
Explanation:
We are given;
Annual deposit; A = $1000
Interest rate; i = 8% = 0.08
Number of years; n = 3
The value of the annuity after 3 years will be gotten from the formula;
FV = A[((1 + i)ⁿ - 1)/i](1 + i)
FV = 1000(((1 + 0.08)³ - 1)/0.08)(1 + 0.08)
FV = 1000(1.08⁴ - 1.08)/0.08
FV = $3506.112
Since you deposited $1000 each year, then after 3 years, total deposited = 3 × 1000 = $3000
Since FV = $3506.112, then interest = $3506.112 - $3000
Interest = $506.112
762 miles = 1226.32 kilometers
you multiply the miles by 1.609 to get the kilometers