Answer:
On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.
Step-by-step explanation:
Given that, the rate R(t) at which cars enter the highway is given the formula
The average rate of car enter the highway during first half hour of rush hour is the average value of R(t) from t=0 to t=30.
![=[100(t-0.0001\frac{t^3}{3})]_0^{30}](https://tex.z-dn.net/?f=%3D%5B100%28t-0.0001%5Cfrac%7Bt%5E3%7D%7B3%7D%29%5D_0%5E%7B30%7D)
![=100[(30-0.0001\frac{30^3}{3})-(0-0.0001\frac{0^3}{3})]](https://tex.z-dn.net/?f=%3D100%5B%2830-0.0001%5Cfrac%7B30%5E3%7D%7B3%7D%29-%280-0.0001%5Cfrac%7B0%5E3%7D%7B3%7D%29%5D)
=2901
The average rate of car is 
=97
On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.
Answer:
Explanation:
The table that shows the pattern for this question is:
Time (year) Population
0 40
1 62
2 96
3 149
4 231
A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.
Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.
Thus you must find both P₀ and r.
<u>1) P₀ </u>
Using the first term of the sequence (0, 40) you get:
P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀
Then, P₀ = 40
<u> 2) r</u>
Take two consecutive terms of the sequence:
- P(1) / P(0) = 40r / 40 = 62/40
You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55
<u>3) Model</u>
Thus, your model is P(x) = 40(1.55)ˣ
<u> 4) Population of moose after 12 years</u>
- P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.
Answer:
x = -8
Step-by-step explanation:
1) 5x + 7= 7x +23
Move the terms
2) 5x + 7 -7x = 23
Collect like terms
3) 5x -7x = 23 - 7
Calculate
4) -2x = 16
Divide both sides by <em>-2</em>
5) x = -8
Answer:
x=-3
Step-by-step explanation:
F(x) just means X.
0=x+3
0-3=x+3-3
-3=x
Answer:
x=6
Step-by-step explanation:
x + 6 = x + x original problem
x + 6 = 2x combine like terms
-x = -x subtract x from both sides to have like terms on each side
6 = x solution
