calculus help please i was sick for a month and now i cant do any of these please explain?

Question

1. put the function in the form P=Poe^kt
P=132(0.2)^t
Po=?
k=?

2.find a solution to the equation if possible.
1=10cos(3x+1)-4

3.nikki invested 12000 in the stock market. it was a loser declining in value 10% eah year for 10 years.how much was the investment worth after 10 years?(exponential function)

after 10 years the stock began to gain value at 10% per year. how long will it take for the investment to regain original value?

4.a town connected to a water supply is billed a fixed amount yearly plus a charge fir each cubic foot of water used. a household using 1000 cubic feet was billed $80 and one using 1600 cubic feet was charged 115.

what is the charge per cubic foot?
write an equation for c, the total cost of a residents water as a fuction of w cubic feet of water used.
how many cubic feet of water used would lead to a bill of $160

5. P=15e^0.85

P=Po(a^t)
what are the values of Po and a?
does this function represent growth or decay?

please explain answers!

Answer 1

(0.2)^t = e^t*ln0.2 so Po=132 and k=ln0.2
2) cos (3x+1)=1/2 so 3x+1= pi/3 +2kpi and 3x+1= -pi/3+2kpi
so x=1/3(pi/3-1)+2kpi/3 and x = 1/3(-pi/3-1)+2kpi/3 (k any integer 12.000(0.9)^10=$4184.14
(4184.14)(1.10)^x=12.000 so 1.10^x= 12000/4184.14
and x= 11.05 (11 years) x= log 12000/418/log 1.1
4)80 = C +1000*w
115= C +1600*w
35= 600x so w= $7/120 per cubic foot
P=15 e^0.85t so e^0.85=a=2.34 and Po = 15
As a>1 it´s a growth
No more explanations needed