Question

The function p(t)=100/1 400xe-0.15t describes how to find the percentage of families who recycle. p(t), in relation to any time t, where t is the number of years after 1960. According to this information, what was the percentage of families who recycled in 1990? (Round your answer to the nearest hundredth)

Answer 1

The percentage of families who recycled in 1990 is approximately 0.00%.

Step-by-step explanation:

To find the percentage of families who recycled in 1990, we need to substitute the value of t with (1990-1960) in the given function p(t) = 100/1400xe^(-0.15t):

p(1990) = 100/1400e^(-0.15(1990-1960))

= 100/1400e^(-0.15(30))

= 100/1400e^(-4.5)

Using a calculator, evaluate e^(-4.5) to get approximately 0.0111.

Therefore, p(1990) is approximately 100/1400 * 0.0111 = 0.0000079.

To convert this to a percentage, multiply by 100: 0.0000079 * 100 = 0.00079%.

Rounding this to the nearest hundredth, the percentage of families who recycled in 1990 is approximately 0.00%.