Solve by back-calculating for the missing number . . . (58 - 7 - 14 + 3)/(5 × 2) = 4
<span>So we have a problem with two unknows and one equation. We have to express one over the other like this: 7a - 2b = 5a + b. First we separate one kind on the left side and the other kind on the right side: 7a - 5a = b + 2b. Then: 2a = 3b. Now we divide both sides by 2 and get: a= 3b/2.</span>
I would need to know the amount of $ the rental life jackets and canoe are.
All you do is multiply 22 times 8 which is 176 then you multiply 8*4
A)
![\bf 1990-1910=80\leftarrow t \\\\\\ P(t)=8000(2)^{-\frac{t}{29}}\implies P(80)=8000(2)^{-\frac{80}{29}} \\\\\\ P(80)=8000\cdot \cfrac{1}{2^{\frac{80}{29}}}\implies P(80)=\cfrac{8000}{\sqrt[29]{2^{80}}}](https://tex.z-dn.net/?f=%5Cbf%201990-1910%3D80%5Cleftarrow%20t%0A%5C%5C%5C%5C%5C%5C%0AP%28t%29%3D8000%282%29%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%5Cimplies%20P%2880%29%3D8000%282%29%5E%7B-%5Cfrac%7B80%7D%7B29%7D%7D%0A%5C%5C%5C%5C%5C%5C%0AP%2880%29%3D8000%5Ccdot%20%5Ccfrac%7B1%7D%7B2%5E%7B%5Cfrac%7B80%7D%7B29%7D%7D%7D%5Cimplies%20P%2880%29%3D%5Ccfrac%7B8000%7D%7B%5Csqrt%5B29%5D%7B2%5E%7B80%7D%7D%7D)
and surely you know how much that is.
b)
![\bf P(t)=125\\\\\\ 125=8000(2)^{-\frac{t}{29}}\implies \cfrac{125}{8000}=2^{-\frac{t}{29}}\implies \cfrac{1}{64}=2^{-\frac{t}{29}} \\\\\\ \textit{now we take log to both sides} \\\\\\ log\left( \frac{1}{64} \right)=log\left( 2^{-\frac{t}{29}} \right)\implies log\left( \frac{1}{64} \right)=-\frac{t}{29}log\left( 2 \right) \\\\\\ log\left( \cfrac{1}{64} \right)=-\cfrac{tlog(2)}{29}\implies \cfrac{-29log\left( \frac{1}{64} \right)}{log(2)}=t\implies 174=t](https://tex.z-dn.net/?f=%5Cbf%20P%28t%29%3D125%5C%5C%5C%5C%5C%5C%20%20125%3D8000%282%29%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%5Cimplies%20%5Ccfrac%7B125%7D%7B8000%7D%3D2%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B64%7D%3D2%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bnow%20we%20take%20log%20to%20both%20sides%7D%0A%5C%5C%5C%5C%5C%5C%0Alog%5Cleft%28%20%5Cfrac%7B1%7D%7B64%7D%20%5Cright%29%3Dlog%5Cleft%28%202%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%20%5Cright%29%5Cimplies%20log%5Cleft%28%20%5Cfrac%7B1%7D%7B64%7D%20%5Cright%29%3D-%5Cfrac%7Bt%7D%7B29%7Dlog%5Cleft%28%202%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0Alog%5Cleft%28%20%5Ccfrac%7B1%7D%7B64%7D%20%5Cright%29%3D-%5Ccfrac%7Btlog%282%29%7D%7B29%7D%5Cimplies%20%5Ccfrac%7B-29log%5Cleft%28%20%5Cfrac%7B1%7D%7B64%7D%20%5Cright%29%7D%7Blog%282%29%7D%3Dt%5Cimplies%20174%3Dt)
since in 1910 t = 0, 174 years later from 1910, is 2084, so in 2084 they'll be 125 exactly, so the next year, 2085, will then be the first year they'd fall under that.