The local museum had 20000 visitors in 1990 . The number of visitors has decreased by 3% each year since 1990 . Enter a function

Question

2 months ago

11

m(x) to represent the number of visitors to the museum x years after 1990

2 answers:

Zina [12.3K] · Answer 1 · 2026-03-17T13:34:23+03:00

Answer:

$m(x)=20,000\cdot (0.97)^x$

Step-by-step explanation:

Recognizing that the local museum attracted 20,000 visitors in 1990, it has since seen a steady 3% decrease annually.

We will utilize an exponential model to formulate a solution, as the decline in visitors follows an exponential pattern.

An exponential function generally follows the format $f(x)=a\cdot b^x$ , where

a = initial quantity,

and b = decay factor in the form of (1-r), with r being the rate expressed in decimal.

$3\%=\frac{3}{100}=0.03$ When we input our values into this formula, we arrive at

$m(x)=20,000\cdot (1-0.03)^x$

$m(x)=20,000\cdot (0.97)^x$

Therefore, the function $m(x)=20,000\cdot (0.97)^x$ serves to indicate the number of museum visitors x years post-1990.

babunello [11.8K] · Answer 2 · 2026-03-17T13:38:20+03:00

Answer:

The function is represented as m(x) = 20,000(0.97)^x.

Step-by-step explanation:

After the year 1990, each year witnesses a decline in visitors, having retained (100-3) = 97% (or 0.97) of the previous year's visitors.

Thus, the model can be expressed as m(x) = 20,000(0.97)^x (final answer).