Question

calculators are allowed on this portion of the test.

1. the number of people visiting a museum is decreasing by 3% a year. this year, there were 50000 visitors. assuming the decline continues, write an equation that can be used to find v, the number of visitors there will be in t years time. 1 mark

Explanation:

Step1: Identify remaining visitor percentage

Since the number decreases by 3% annually, the remaining percentage of visitors each year is $100\% - 3\% = 97\% = 0.97$.

Step2: Set up exponential decay formula

This is an exponential decay problem, where the initial number of visitors $V_0 = 50000$, the decay factor is $0.97$, and time is $t$ years. The general form for exponential decay is $V = V_0 \times (\text{decay factor})^t$.
Substitute the known values:
$V = 50000 \times (0.97)^t$

Answer:

$V = 50000(0.97)^t$