Okay so uh i think it’s this: 15% of 60=0.15* 60=9
9 is what percent of 180 i think..?
9/180=1/20=5/100=5%
Answer: 1211.6585 years
<u>Step-by-step explanation:</u>
The equation for exponential growth is: ![P=P_oe^{kt}](https://tex.z-dn.net/?f=P%3DP_oe%5E%7Bkt%7D)
- P: final population
- P₀: initial population
- k: rate of decay (or growth)
- t: time
Use the half life information to find k:
![\dfrac{1}{2}P_o=P_oe^{k(800)}\\\\\\\dfrac{1}{2}=e^{800k}\qquad \rightarrow \qquad \text{divided both sides by}\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=800k\qquad \rightarrow \qquad \text{applied ln to both sides}\\\\\\\dfrac{ln(\frac{1}{2})}{800}=k\qquad \rightarrow \qquad \text{divided both sides by 800}\\\\\\\large\boxed{-0.000867=k}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7DP_o%3DP_oe%5E%7Bk%28800%29%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B2%7D%3De%5E%7B800k%7D%5Cqquad%20%5Crightarrow%20%5Cqquad%20%5Ctext%7Bdivided%20both%20sides%20by%7D%5C%20P_o%5C%5C%5C%5C%5C%5Cln%5Cbigg%28%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%3D800k%5Cqquad%20%5Crightarrow%20%5Cqquad%20%5Ctext%7Bapplied%20ln%20to%20both%20sides%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bln%28%5Cfrac%7B1%7D%7B2%7D%29%7D%7B800%7D%3Dk%5Cqquad%20%5Crightarrow%20%5Cqquad%20%5Ctext%7Bdivided%20both%20sides%20by%20800%7D%5C%5C%5C%5C%5C%5C%5Clarge%5Cboxed%7B-0.000867%3Dk%7D)
Next, input the information (65% decayed = 35% remaining) and the k-value to find your answer.
![.35P_o=P_oe^{-0.000867t}\\\\\\.35=e^{-0.000867t}\\\\\\ln(.35)=-0.000867t\\\\\\\dfrac{ln(.35)}{-0.000867}=t\\\\\\\large\boxed{1211.6585=t}](https://tex.z-dn.net/?f=.35P_o%3DP_oe%5E%7B-0.000867t%7D%5C%5C%5C%5C%5C%5C.35%3De%5E%7B-0.000867t%7D%5C%5C%5C%5C%5C%5Cln%28.35%29%3D-0.000867t%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bln%28.35%29%7D%7B-0.000867%7D%3Dt%5C%5C%5C%5C%5C%5C%5Clarge%5Cboxed%7B1211.6585%3Dt%7D)
angle ABE is equivalent
to the whole angle, and it measures 2b. <span>
while the angle ABF is only a portion of angle ABE, and it
measure 7b - 24.
<span>since we know the measure of the whole angle and a part of
the angle, we can then subtract to find the left over angle (angle EBF), so
Angle EBF = Angle ABE - Angle ABF </span></span>
Angle EBF = 2b – (7b –
24)
<span>Angle EBF = 24 – 5b</span>