contestada

The yearly attendance at a local restaurant is 42,400 Grows continuously at a rate of 4.1% each year what is the approximate attendance at the restaurant in 15 years

Respuesta :

apologiabiology
compounded continuously

neato

A=Pe^(rt)
r=rate=4.1%=0.041
P=principal=42400
t=time=15

A=42400e^(0.041*15)
A=42400e^(0.615)
A=78425.4

so the attendance is about 78425 people

Answer:

$78,425.44

Step-by-step explanation:

We have been given that the yearly attendance at a local restaurant is 42,400 Grows continuously at a rate of 4.1% each year.

We will continuous compound interest formula to solve our given problem.

[tex]A=P\cdot e^{rt}[/tex], where,

A = Final amount,

P = Initial amount,

r = Rate in decimal form,

t = Time.

[tex]4.1\%=\frac{4.1}{100}=0.041[/tex]

Substitute the given values:

[tex]A=\$42,400\cdot e^{0.041*15}[/tex]

[tex]A=\$42,400\cdot e^{0.615}[/tex]

[tex]A=\$42,400\cdot 1.849656599558327[/tex]

[tex]A=\$78,425.43982[/tex]

[tex]A\approx \$78,425.44[/tex]

Therefore, the attendance at the restaurant in 15 years would be $78,425.44.