The equation N(t) = 400/1+39e^(-7)t models the number of people N in a town who have heard a rumor after t days.
To the nearest whole number, how many people will have heard the rumor after 3 days?
Weird, the bot got 2 different wrong answers for the same question, lol
To find the number of people who have heard the rumor after 3 days, we can plug in t = 3 into the equation N(t) = 400 / (1 + 39e^(-7t)) and round the result to the nearest whole number.
N(3) = 400 / (1 + 39e^(-7 * 3))
= 400 / (1 + 39e^(-21))
Now we need to evaluate e^(-21) using a calculator:
≈ 400 / (1 + 39 * 8.28947 * 10^(-10))
≈ 400 / (1 + 3.23014 * 10^(-8))
≈ 400 / 1.0000000323014
≈ 399.9999980764083
Rounding the result to the nearest whole number:
≈ 400
Therefore, the nearest whole number of people who will have heard the rumor after 3 days is 400.
To find out how many people will have heard the rumor after 3 days, we need to substitute t = 3 into the equation N(t) = 400 / (1 + 39e^(-7t)).
Let's start by evaluating the exponent part: e^(-7t). Substitute t = 3 into this part:
e^(-7 * 3) = e^(-21).
Now, calculate e^(-21). e is a mathematical constant approximately equal to 2.71828, and the exponent (-21) represents the power to which e is raised. Using a calculator or mathematical software, evaluate e^(-21) = 0.000000000000207.
Next, substitute the calculated value of e^(-21) back into the original equation:
N(t) = 400 / (1 + 39 * 0.000000000000207).
Multiply 39 by 0.000000000000207:
39 * 0.000000000000207 = 0.000000000008073.
Now, substitute this result back into the equation:
N(t) = 400 / (1 + 0.000000000008073).
Add 1 to 0.000000000008073:
1 + 0.000000000008073 = 1.000000000008073.
Finally, divide 400 by 1.000000000008073:
N(t) = 400 / 1.000000000008073.
The result of this division is approximately 399.999999999918, which, when rounded to the nearest whole number, is 400.
Therefore, to the nearest whole number, approximately 400 people will have heard the rumor after 3 days.
To solve the problem, we can substitute t=3 into the equation and solve for N:
N(3) = 400 / (1 + 39e^(-7*3))
N(3) ≈ 221
Therefore, to the nearest whole number, we can say that about 221 people will have heard the rumor after 3 days.