(Solved): 8. A certain lake is stocked with 10,000 fish. The population is growing according to the logistics ...

8. A certain lake is stocked with 10,000 fish. The population is growing according to the logistics curve: $$p\frac{10,000}{19e^{\frac{t}{5}}}$$ where $$t$$ is measured in months since the lake was initially stocked. a. Find the population in 8 months b. How many months will the fish population going to be 2000 . 9. The population of city is given by $$P100,000(1.03{)}^t$$ where $$t$$ is the number of years after 1988 . Find the population in (a) 1988 (b) 1989 and (c) 1990. 10. A radioactive element is such that $$\mathrm{N}$$ grams remain after $$\mathrm{t}$$ hours, where $$N20e^{0.028t}$$. How many grams remain after 30 hours? 11. Problem (a) - (c), find (i) the compound amount and (ii) the compound interest for the given investment and annual rate. a. RM4000 for 7 years at $$6\%$$ compounded annually b. RM700 for 15 years at $$7\%$$ compounded semiannually c. RM4000 for 15 years at $$81/2\%$$ compounded quarterly d. RM5000 for $$21/2$$ years at $$9\%$$ compounded monthly e. RM8000 for 3 years at $$61/4\%$$ compounded daily. (Assume that there are 365 days in a years). 12. A trust fund is being set up by a single payment so that at the end of 30 years there will be RM20,000 in the fund. If the interest rate is $$8\%$$ compounded quarterly, how much money should be paid initially into the trust fund?