Given:
Initially the number of people at art museum = 250
Rate of increase = 3% per month
To find:
The number of people at art museum in the end of a year.
Solution:
The general exponential growth model is:
[tex]y=a\left(1+\dfrac{r}{100}\right)^t[/tex]
Where, a is the initial value, r is the rate of increase in % and t is the time period.
We know that, 1 year = 12 months.
Putting a=250, r=3 and t=12, we get
[tex]y=250\left(1+\dfrac{3}{100}\right)^{12}[/tex]
[tex]y=250\left(1+0.03\right)^{12}[/tex]
[tex]y=250\left(1.03\right)^{12}[/tex]
[tex]y=250(1.42576)[/tex]
[tex]y=356.44[/tex]
[tex]y\approx 356[/tex]
The number of people at the end of a year is 356. Therefore, the correct option is D.
