Answer:
The year in which there are 30 m² of agricultural land available for each inhabitant is approximately 438.286 years
Step-by-step explanation:
The growth rate of the planet Magrathea = Double every 40 years
The start population of Magrathea = 20 million
The area of the Magrathea = 200 million km²
The area that can hose 200 Magratheans = 1 km²
The land used for agriculture = The land not used for housing
The equation for a population that doubles every 20 years is given as follows;


We have;

㏑2 = 40·㏑(1 + r)
㏑(1 + r) = ㏑(2)/40
1 + r = ㏑(2)/40
1 + r = e^(㏑(2)/40)
r = 1 - e^(㏑(2)/40) = 0.0174796921
30 m²
200·x
The area per individual = (1/200) km²
The total number
We have;
(x/200) km²) + (x × 0.00003 km²) = 200,000,000 km²
x × ((1/200) km² + 0.00003 km²) = 200,000,000 km²
x = 200,000,000 km²/(((1/200) km² + 0.00003 km²)) = 3.97614314 × 10¹⁰
The population at the time = 3.97614314 × 10¹⁰
We have;
3.97614314 × 10¹⁰/(2×10⁷) = 
t = ㏑((3.97614314 × 10¹⁰/(2×10⁷)))/(㏑
)) ≈ 438.286 years
The year in which there are 30 m² of agricultural land available for each inhabitant ≈ 438.286 years