1. An investment of 3000 dollars grows according to the model $A(t) = 3000(1.05)^t$. Find the time $t$ in years for the investment to reach 6000 dollars. Round to the nearest whole year. $t = $ ___.
2. A town's population is decreasing according to the model $P(t) = a(0.90)^t$. If the population after 4 years is 6,561, what was the initial population, $a$? $a = $ ___.
3. An initial investment of 2500 dollars grows to 3200 dollars in 5 years. Given the model $A(t) = 2500(1 + r)^t$, what is the approximate annual growth rate $r$?
4. To solve the equation $450 = 150(1.04)^t$ for $t$, what is the correct first algebraic step?
5. A substance decays according to the model $M(t) = 80(0.75)^t$, where $M$ is mass in grams. How many hours, $t$, will it take for the mass to reduce to 10 grams? Round to one decimal place. $t = $ ___.
6. A camera costs 90 dollars now, and the inflation rate is 6% annually. How long will it be before the camera costs 120 dollars? (Round to one decimal place) ___ years.
7. The population of a town is given by $P(t) = 3800 \cdot 2^{-t/20}$, where $t$ is the number of years since 1910. In what year did the population first dip below 120? The year is ___.
8. A sofa costs 1200 dollars now, and the inflation rate is 8% annually. How much will the sofa cost 20 months from now? (Round to two decimal places) ___ dollars.
9. A sofa costs 1200 dollars now, and the inflation rate is 8% annually. How long will it be before the sofa costs 1500 dollars? (Round to one decimal place) ___ years.