Answer:
33.6 square meters
Step-by-step explanation:
a. The area doubles each week, starting with 12.5 square meters.
12.5, 25, 50, 100, 200, ...
We can model this as a geometric sequence, where the first term is 12.5 and the common ratio is 2. The nth term of the sequence is:
aₙ = a₀ (r)^n
aₙ = 12.5 (2)^n
This is the area after n weeks. We can find the daily area by dividing the exponent by 7.
a = 12.5 (2)^(d/7)
where d is the number of days.
So the area after 10 days is:
a = 12.5 (2)^(10/7)
a ≈ 33.6
b. Using exponent properties, we can rewrite the equation as:
a = 12.5 (2)^(d/7)
a = 12.5 (2^(1/7))^d
So after 1 day, the area increases by a factor of 2^(1/7) (seventh root of 2).
