Suppose that a fungal disease originates in the middle of an orchard, initially affecting only one tree. The disease spreads out radially at a constant speed of 45 feet per day.

(a) What area will be affected after 2 days?

(b) What area will be affected after 4 days?

(c) What area will be affected after 8 days?

(d) Write a formula for the affected area as a function of time, measured in days. Use t as your variable for time, in days.

a) 25446.90 ft²

b) 101787.60 ft²

c) 407150.41 ft²

d) 2025πt²

Step-by-step explanation:

Data provided in the question:

Rate of spread radially = 45 feet per day

a) Radius of spread after 2 days

= 45 * 2

= 90 feet

Therefore,

Area affected = πr²

= π (90) ²

= 25446.90 ft²

b) Radius of spread after 2 days

= 45 * 4

= 180 feet

Therefore,

Area affected = πr²

= π (180) ²

= 101787.60 ft²

c) Radius of spread after 2 days

= 45 * 8

= 360 feet

Therefore,

Area affected = πr²

= π (360) ²

= 407150.41 ft²

a) Radius of spread after t days

= 45 * t ft

Therefore,

Area affected = πr²

= π (45t) ²

= 2025πt²