Question

The function f left parenthesis x right parenthesis equals 60 e Superscript negative 0.7 x Baseline plus 40 describes the percentage of​ information, f(x), that a particular person remembers x weeks after learning the information.

a. nbsp Substitute 0 for x​ and, without using a​ calculator, find the percentage of information remembered at the moment it is first learned. nbsp Bold
b. nbsp Substitute 1 for x and find the percentage of information that is remembered after 1 week. nbsp Bold
c. Find the percentage of information that is remembered after 8 weeks. Bold
d. nbsp Find the percentage of information that is remembered after one year​.

Answer 1

a. The percentage of information remembered at the moment it is first learned is 100%. b. The percentage of information remembered after 1 week is approximately 29.796%. c. The percentage of information remembered after 8 weeks is approximately 41.076%.

Step-by-step explanation:

a. To find the percentage of information remembered at the moment it is first learned, substitute 0 for x in the given function. This gives us f(0) = 60e-0.7(0) + 40. Since any number raised to the power of 0 is equal to 1, the equation simplifies to f(0) = 60(1) + 40. Therefore, the percentage of information remembered at the moment it is first learned is 60 + 40 = 100%.

b. To find the percentage of information remembered after 1 week, substitute 1 for x in the given function. This gives us f(1) = 60e-0.7(1) + 40. Calculating this gives us f(1) ≈ 60(0.4966) + 40. Therefore, the percentage of information remembered after 1 week is approximately 29.796%.

c. To find the percentage of information remembered after 8 weeks, substitute 8 for x in the given function. This gives us f(8) = 60e-0.7(8) + 40. Calculating this gives us f(8) ≈ 60(0.0346) + 40. Therefore, the percentage of information remembered after 8 weeks is approximately 41.076%.

d. To find the percentage of information remembered after one year, substitute 52 for x in the given function. This gives us f(52) = 60e-0.7(52) + 40. Calculating this gives us f(52) ≈ 60(0.000000025) + 40. Therefore, the percentage of information remembered after one year is approximately 40.0000025%.