Question

Pls help

About 3,500 tourists visit the Granite Falls overlook each year. After the construction of a new nature center with exhibits and hands-on activities, that number is expected to increase 5% each year. Assuming the same growth continues, you can use a function to approximate the number of annual visitors to the overlook x years after the nature center is built.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.

Answer 1

Explanation:

Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:

Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:

y0 = 3,500

Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:

r = 0.05

Write the equation for exponential growth. The formula for exponential growth is given by:

y = y0 × (1 + r)^x

where x is the number of years after the nature center is built.

So, the equation for the function in this case would be:

f(x) = 3,500 × (1 + 0.05)^x

This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.