Sam invests $4,000 in an account that earns 2.5% interest compounded continuously. to determine the amount in the account after a specified amount of time, sam uses the equation a = p e r t where a is the amount of money in the account after t years, p is the principal, and r is the rate of interest. sam has a goal of having an account balance of $12,000. which logarithmic equation can sam use to determine the number of years it will take to reach his goal? a. t = ln 3 0 . 025 b. t = 3 ln 0 . 025 c. t = 12 , 000 ( ln 4000 0 . 025 ) d. t = 3 ln 0 . 025

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)