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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.

Respuesta :

Answer:

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

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