Question

The attendance at the art museum at the New Year's opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year? 1329 5825 265 356
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Answer 1

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:

$y=a\left(1+\dfrac{r}{100}\right)^t$

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

$y=250\left(1+\dfrac{3}{100}\right)^{12}$

$y=250\left(1+0.03\right)^{12}$

$y=250\left(1.03\right)^{12}$

$y=250(1.42576)$

$y=356.44$

$y\approx 356$

The number of people at the end of a year is 356. Therefore, the correct option is D.