Question

Jen is a biologist studying endangered and at-risk species in Mongolia. When she first started studying the snow leopard population, she estimated that there were 1,000 snow leopards in Mongolia. After one year, Jen estimated that the population had decreased to 990. She expects the snow leopard population to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the estimated snow leopard population in Mongolia, y, in x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =

To the nearest whole number, how many snow leopards can Jen expect there to be in Mongolia in 5 years?

Answer 1

To model the estimated snow leopard population in Mongolia using an exponential equation of the form \( y = a(b)^x \), we need to define the values for \( a \) and \( b \):

1. **Initial Population (\( a \))**: This represents the estimated initial population of snow leopards, which is 1,000. So, \( a = 1000 \).

2. **Growth/Decay Factor (\( b \))**: The population decreased from 1,000 to 990 in one year. To find the decay factor \( b \):

\[
b = \frac{\text{Population after 1 year}}{\text{Initial population}} = \frac{990}{1000} = 0.99
\]

Now we can write the exponential equation:

\[
y = 1000(0.99)^x
\]

### Estimate the population in 5 years:

To find the population after 5 years (\( x = 5 \)), substitute \( x \) into the equation:

\[
y = 1000(0.99)^5
\]

Calculating \( (0.99)^5 \):

\[
(0.99)^5 \approx 0.95099005
\]

Now multiply by 1,000:

\[
y \approx 1000 \times 0.95099005 \approx 950.99
\]

Rounding to the nearest whole number:

\[
y \approx 951
\]

Thus, Jen can expect there to be approximately **951 snow leopards in Mongolia in 5 years**.

In summary, the modeled equation is:
\[
y = 1000(0.99)^x
\]
And after 5 years, Jen can expect about **951 snow leopards**.