This is the concept of differential equations, given that
dp/dt=rp
then:
dp/p=rdt
thus:
ln p=rt+C
p=e^(rt+C)
P=Ke^(rt)
when t=210 days=7 months, p=2k
2k=k×e^(7r)
2=e^(7r)
ln2=7r
r=ln(2)/7
r=0.0990
7(10 visits) ≤ 68
70 ≤ 68
Not Viable
7(9 visits) ≤ 68
63 ≤ 68
Viable
The first solution is not viable because 10 visits will give a total cost of $70 per month, which is $2 over his monthly budget of $68.
The second solution is viable. He could visit the gym a maximum of 9 times per month for a total of $63 a month and that will be under his $68 monthly budget.
Hope this helps! :)
Answer: the answer to number seven is x=3
Step-by-step explanation:
