Question

A population of deer is increasing exponentially. Which exponential equation in the form y=abx
represents the situation shown in the graph?

Answer 1

To write the exponential equation \( y = ab^x \) that represents the situation shown in a graph of a population of deer increasing exponentially, you'll need two key pieces of information from the graph:

1. **Initial value (a):** This is the value of the population at time \( x = 0 \). This represents your starting number of deer. You can find this value on the y-axis of the graph.

2. **Growth factor (b):** This is determined by how much the population increases over a specific interval of time (commonly one unit of time). You might find this by examining the population at two different points in time and using the formula for exponential growth.

If the graph provides specific points, for example, if at \( x = 0 \) the population is 50 and at \( x = 1 \) the population is 100, you can calculate \( b \) as follows:

1. Use the initial value \( a = 50 \).
2. You know that:
\[
y = ab^x
\]
At \( x = 1 \), \( y = 100 \):
\[
100 = 50b^1
\]
\[
100 = 50b \implies b = 2
\]

With these values, your equation would be:
\[
y = 50(2^x)
\]

If you have specific values from the graph, please provide them, and I can help determine \( a \) and \( b \) more accurately!