Question

1. ice on a lake gets thicker as long as the temperature is below freezing. on a certain lake it took 8 days for the ice to reach a thickness of 3 inches.

(a) at what rate was the ice growing over these 8 days in inches per day? do not round your decimal answer.
(b) ice is safe to walk on when it is 10 inches thick. would this ice be safe after 3 weeks if it grew at the rate in (a)?

Explanation:

Step1: Calculate growth rate

The growth rate $r$ is calculated by dividing the total thickness by the number of days. Given thickness $t = 3$ inches and number of days $n=8$. So $r=\frac{t}{n}=\frac{3}{8}$ inches per day.

Step2: Calculate thickness in 3 weeks

3 weeks have $3\times7 = 21$ days. Using the rate $r=\frac{3}{8}$ inches per day, the thickness $T$ in 21 days is $T=r\times21=\frac{3}{8}\times21=\frac{63}{8}= 7.875$ inches.

Step3: Compare with safe - thickness

Since $7.875<10$, the ice is not safe to walk on.

Answer:

(a) $\frac{3}{8}$ inches per day
(b) No