The yearly attendance at a local movie theatre is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theatre in nine years?
A: 57,789
B: 77,789
C: 81,096
D: 81,724
56000 (1 + .042)^9 =81.724
56000 (1 + .042)^9
oooo nevermind
To find the approximate attendance at the movie theatre in nine years, we can use the formula for continuous exponential growth:
N = P * e^(rt)
Where:
N = final attendance
P = initial attendance
r = growth rate (as a decimal)
t = time (in years)
e = mathematical constant approximately equal to 2.71828
Given:
P = 56,000
r = 4.2% = 0.042
t = 9
Substituting these values into the formula, we have:
N = 56,000 * e^(0.042 * 9)
Now, let's calculate it step by step.
Firstly, we multiply the growth rate and time:
0.042 * 9 = 0.378
Next, we calculate e^(0.378) using a calculator or computer software. This exponentiation value depends on the platform you are using. Let's assume we're using a calculator that automatically uses e as the base.
e^(0.378) ≈ 1.45942
Now, we multiply the initial attendance by the result:
56,000 * 1.45942 ≈ 81,724.72
Therefore, the approximate attendance at the movie theatre in nine years is approximately 81,724.
The correct answer is option D: 81,724.
1) C. 25
2) B. a_n=a_n-1+(n-1)^2
3) B. %35,568.95
4) D. $7,403.66
5) D. 81,724
6) A. 22,149
100% correct Growth and Decay AQR