Answer:
![n \geq -\frac{-29}{28}](https://tex.z-dn.net/?f=n%20%5Cgeq%20%20-%5Cfrac%7B-29%7D%7B28%7D)
Step-by-step explanation:
![-3(1 - 7n) \geq -32 - 8n\\-3 + 21n \geq -32 -8n\\](https://tex.z-dn.net/?f=-3%281%20-%207n%29%20%5Cgeq%20%20-32%20-%208n%5C%5C-3%20%2B%2021n%20%5Cgeq%20%20-32%20-8n%5C%5C)
+8n +8n
![-3 + 28n \geq -32\\+3 +3\\28n \geq -29\\/28 /28\\n \geq \frac{-29}{28}](https://tex.z-dn.net/?f=-3%20%2B%2028n%20%5Cgeq%20%20-32%5C%5C%2B3%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%2B3%5C%5C28n%20%20%5Cgeq%20%20-29%5C%5C%2F28%20%20%20%20%20%20%20%20%20%20%20%20%20%20%2F28%5C%5Cn%20%5Cgeq%20%5Cfrac%7B-29%7D%7B28%7D)
Answer:
It will take about 35.439 years to triple.
Step-by-step explanation:
Recall the formula for continuously compounded interest:
![A=P\,e^{r*t}](https://tex.z-dn.net/?f=A%3DP%5C%2Ce%5E%7Br%2At%7D)
where "A" is the total (accrued or future) accumulated value, "r" is the rate (in our case 0.031 which is the decimal form of 3.1%), "P" is the principal, and "t" is the time in years (our unknown).
Notice also that even that the final amount we want to get is three times $48,000. So our formula becomes:
![3\,*\,48,000=\,48,000\,\,e^{0.031\,*t}\\\frac{3\,*\,48,000}{48,000} =e^{0.031*t}\\3=e^{0.031*t}](https://tex.z-dn.net/?f=3%5C%2C%2A%5C%2C48%2C000%3D%5C%2C48%2C000%5C%2C%5C%2Ce%5E%7B0.031%5C%2C%2At%7D%5C%5C%5Cfrac%7B3%5C%2C%2A%5C%2C48%2C000%7D%7B48%2C000%7D%20%3De%5E%7B0.031%2At%7D%5C%5C3%3De%5E%7B0.031%2At%7D)
Now,in order to solve for "t" (which is in the exponent, we use logarithms:
![ln(3)=0.031\,*\,t\\t=\frac{ln(3)}{0.031} \\t=35.439 \,\,years](https://tex.z-dn.net/?f=ln%283%29%3D0.031%5C%2C%2A%5C%2Ct%5C%5Ct%3D%5Cfrac%7Bln%283%29%7D%7B0.031%7D%20%5C%5Ct%3D35.439%20%5C%2C%5C%2Cyears)
For number 12 the answer is 15.36
3 pairs of choices give rise to 2^3 = 8 possibilities:
.. bus, full, morning
.. bus, full, afternoon
.. bus, concession, morning
.. bus, concession, afternoon
.. train, full, morning
.. train, full, afternoon
.. train, concession, morning
.. train, concession, afternoon
A-4b that’s my answer hope this help