Math Questions! Help ASAP

Question

Question 1:

The average cost of a scientific calculator was $96.50 in 1970. The same type of calculator cost $22 in 2016. Assuming the exponential decay model applies, what will a similar calculator cost in the year 2023? Round your answer to the nearest cent.

Question 2:

Part A:

Reshanda was invited for coffee at 2:00 pm, but she normally goes to sleep at 10:00 pm. If a 16-oz coffee has 122 mg of caffiene, and the half-life of caffiene is 5.5 hours, how much caffiene would still be in her system at bedtime? (Round your answer to the nearest tenth of a milligram)

Part B:

Suppose Reshanda cannot sleep if she has 15 or more mg of caffeine in her system. How many hours before she goes to sleep could she drink a 16-oz coffee? (Round your answer to the nearest tenth of an hour)

Answer 1

A = Pe^rt

96.5 =95.5e^r(0)= 95.5e^0 = 95.5(1) at time t=0r

22 = 95.5e^46r

22/95.5 = e^46r

ln(22/95.5) = 46r

r = ln(22/95.5)/46

r = about -3.19% decay rate

7 years later, in 2023

A = 95.5e^(ln(22/95.5)/(46+7))

= about 95.5e^(53(-.0319))

= about $17.60 = average cost of a scientific calculator in 2023 for a similar calculator (ignoring inflation, especially lately)