Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Step-by-step explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
<h3>(a)</h3>
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
__
<h3>(b)</h3>
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
__
<h3>(c)</h3>
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152
The answer is 87,455
P(x) = P(0) * nˣ
P(x) - the final population after period x
P(0) - the initial population
n - the growth factor in decimal
x - period of time
x = 3 hours
P(3) = 25,143
P(0) = ?
n = 100- 34% = 66% = 0.66
P(x) = P(0) * nˣ
25,143 = P(0) * 0.66³
25,143 = P(0) * 0.287496
P(0) = 25,143 / 0.287496
P(0) ≈ 87,455
Answer:
A. a little more than 1/4 of the students prefer video games
B. I think the most reasonable prediction is 25
329,000 is the nearest thousand of 328,512
Simplifying
3m = 5(m + 3) + -3
Reorder the terms:
3m = 5(3 + m) + -3
3m = (3 * 5 + m * 5) + -3
3m = (15 + 5m) + -3
Reorder the terms:
3m = 15 + -3 + 5m
Combine like terms: 15 + -3 = 12
3m = 12 + 5m
Solving
3m = 12 + 5m
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-5m' to each side of the equation.
3m + -5m = 12 + 5m + -5m
Combine like terms: 3m + -5m = -2m
-2m = 12 + 5m + -5m
Combine like terms: 5m + -5m = 0
-2m = 12 + 0
-2m = 12
Divide each side by '-2'.
m = -6
Simplifying
m = -6
