Question

The size, ???? S , of a tumor (in cubic millimeters) is given by ????=2???? S = 2 t , where ???? t is the number of months since the tumor was discovered. Give units with your answers. (a) What is the size of the tumor right after 9 months?

Answer 1

Answer:

Check Explanation

Step-by-step explanation:

a) S = 2ᵗ

For the first 9 months, we just put t = 0,1,2,3,4,5,6,7,8,9

t = 0

S = 2⁰ = 1 mm³

t = 1 month

S = 2¹ = 2 mm³

t = 2 months

S = 2² = 4 mm³

t = 3 months

S = 2³ = 8 mm³

t = 4 months

S = 2⁴ = 16 mm³

t = 5 months

S = 2⁵ = 32 mm³

t = 6 months

S = 2⁶ = 64 mm³

t = 7 months

S = 2⁷ = 128 mm³

t = 8 months

S = 2⁸ = 256 mm³

t = 9 months

S = 2⁹ = 512 mm³

Right after 9 months, the size of the tumour = 512 mm³

b) Average rate of change in size of the tumor during the first 9 months = [f(b) - f(a)]/(b - a) = (512 - 1)/(9-0) = 56.78 mm³