Question

A person was having a graduation party and noticed that only 5 people were
there after the first hour but grew in size by 61% every hour. If the size of the
party grew this way for 6 hours, how many people would be at the party on
the 6th hour?
Round your answer to the nearest person (whole number).

A. 66
B.87
C. 5031
D. 54

Answer 1

Using an exponential function, it is found that the number of people in the party in the 6th hour was of:

D. 54

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial value.

• r is the growth rate, as a decimal.

In this problem, the parameters are A(0) = 5, r = 0.61, and considering that the first hour is at t = 1, the equation is:

$A(t) = A(0)(1 + r)^{t-1}$

$A(t) = 5(1.61)^{t-1}$

Hence, in the 6th hour:

$A(6) = 5(1.61)^{6-1} = 54$

Which means that option D is correct.

More can be learned about exponential functions at https://brainly.com/question/25537936