Answer to Question #101085 in Algebra for Raunak

Question

A lotus plat initially covers an area of 40cm2. The area is covers increases by 20% each week.
a)Does the area covered by the plant increase by a constant each week
b)Find out the function A(n)which represents the area covered by the lotus plant in n weeks
c)What does the graph of A(n) look like
d)What area is covered by the lotus plant in three weeks
e)How long will it take for the plant to cover an area of 100cm2

Answer 1

a) No.

b)

$$A(n)=40(1.2)^n$$

c) It looks like the exponential function.

d)

$$A(3)=40(1.2)^3=69.12\ cm^2$$

e)

$$100=40(1.2)^x\to x=\log _{1.2}(2.5)$$

$$x\approx 5$$