Note: These answers are approximate. You may have numbers which are slightly different, but they should be in the same ballpark.

1. R = -0.8*T+56.5 where T is temperature in ($^{\circ}F$) and R is the reduction of heart rate in ( $\frac{beats}{min}$).

2. log Q = 0.05*t + 1. So log(1+r) = 0.05, r = 12.2% and log Q$_{\circ}$ = 1, Q$_{\circ}$ = 10. Thus, the final exponential formula is Q = 10*(1.122)$^t$.

3. 1. Linear $\rightarrow$ Q = 0.56*t-0.5
   2. Exponential $\rightarrow$ Q = 7.41*(1.0965)$^t$

Other Homework:

1. $P$ = population in people; $t$ = time in years from 1981; $P_0$ = 35,000; $r$ = ? percentage rate of growth per year. At $t$ = 2000-1981 = 19, we have $P$ = 75,000. So
   
   $$75,000 = 35,000(1+r)^{19}$$
   
   
   and $r$ = 4.1%. To find $P$ at $t$ = 2025-1981 = 43.

   
   

   $$P = 35,000(1+0.041)^{43} = 196,993$$
   
   

2. $P$ = killer bee population; $t$ = time in years from 20 years ago (1980); $P_0$ = killer bee population in 1980; $r$ = ? percentage rate of growth per year. After 20 years $P = 5P_0$ so that

   
   

   $$5P_0 = P_0(1+r)^{20}.$$
   
   

   The $P_0$'s cancel. Taking the 20th root of both sides then subtracting 1 allows us to solve for $r$ ($r = 8.4\%$).

3. Recall

   
   

   $$A = P(1+\frac{APR}{n})^{nY}.$$
   
   

   Here n = 365, and daily compounding = $\frac{APR}{365} = 0.00016$ so

   
   

   $$APY = \frac{year \; end \; amount - year \; start \; amount}{... ...} = \frac{P(1.00016)^{365} - P}{P} = (1.00016)^{365}-1 = 6.0\%$$