Jen is a biologist studying endangered and at-nisk 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 \( y=a(b)^{\prime} \) that can model the estimated snow leopard population in Mongolis, \( y \), in \( \times \) years. Use whole numbers, decimals, or simplified fractions for the values of a and b. \[ y=\square \text {. } \] To the nearest whole number, how many snow leopards can Jen expect there to be in Mongolia in 5 years? snow leopards

\[ \textbf{Step 1: Set Up the Exponential Model} \] The general form of the exponential model is \[ y = a(b)^x, \] where: - \( a \) is the initial population, - \( b \) is the decay factor, - \( x \) is the number of years. Since Jen estimated there were 1,000 snow leopards initially, we have: \[ a = 1000. \] \[ \textbf{Step 2: Determine the Decay Factor \( b \)} \] After 1 year, the population was estimated at 990. Plug \( x = 1 \) and \( y = 990 \) into the model: \[ 990 = 1000(b)^1. \] Solve for \( b \): \[ b = \frac{990}{1000} = 0.99. \] \[ \textbf{Step 3: Write the Exponential Equation} \] The exponential model is: \[ y = 1000(0.99)^x. \] \[ \textbf{Step 4: Estimate the Population in 5 Years} \] To find the population after 5 years, set \( x = 5 \) in the equation: \[ y = 1000(0.99)^5. \] Calculate \( (0.99)^5 \): \[ (0.99)^5 \approx 0.95099. \] Thus, \[ y \approx 1000 \times 0.95099 \approx 950.99. \] \[ \textbf{Step 5: Round the Answer} \] Rounding to the nearest whole number: \[ y \approx 951. \] \[ \textbf{Final Answers:} \] 1. The exponential equation is: \[ y = 1000(0.99)^x. \] 2. In 5 years, Jen can expect there to be approximately 951 snow leopards.