Remark
This problem is done in 2 steps. The first step determines k and the second step is your answer.
Determining K
P = 233 million
A = 231 million
k = ??
t = 1999 - 1991 = 8 years.
Solution
P = Ae^(kt)
233 = 231 * e ^(kt) Divide by 231
233/231 = e^(k8) Do the division
1.008658 = e^(k8) Take the log of both sides.
ln(1.008658) = k8 * ln(e) You are in natural logs. Ln(e) = 1; kt can be brought down and made into a result that is multiplied by ln(e)
ln(1.008658) = 8k Take the ln of 1.008 ...
0.008621 = 8k Divide by 8
k = 0.008621 / 8
k = 0.0011 rounded, but a more accurate number is in the storage area of the calculator.
Now to get the second part.
P = ??
A = 231
k = 0.0011
t = 12
P = 231 * e^(0.0011*12)
P = 231 * e^(0.012931114) using the stored value of M
P = 231 * 1.013015083
P = 234.006 which rounded to the closest million is 234 million
Answer 234 million.
It is b 4/3+2/3 is 6/3 and 6/3 divided by 1/3 is 2/3x
Answer:
x ≥−42
Step-by-step explanation:
x/7 ≥−6
Multiply each side by 7
x/7 * ≥−6*7
x ≥−42
F(x)=2x^2-x-6
Factoring:
f(x)=2(2x^2-x-6)/2=(2^2x^2-2x-12)/2=[(2x)^2-(2x)-12]/2
f(x)=(2x-4)(2x+3)/2=(2x/2-4/2)(2x+3)→f(x)=(x-2)(2x+3)
g(x)=x^2-4
Factoring
g(x)=[sqrt(x^2)-sqrt(4)][sqrt(x^2)+sqrt(4)]
g(x)=(x-2)(x+2)
f(x)/g(x)=[(x-2)(2x+3)] / [(x-2)(x+2)
Simplifying:
f(x)/g(x)=(2x+3)/(x+2)
Answer: Third Option (2x+3)/(x+2)