Question

Rodrigo is an ichthyologist, or a scientist who studies fish. When he first started monitoring the sturgeon population of Lavender Lake, he estimated there were 600 sturgeon in the lake. One year later, Rodrigo estimated the population had decreased to 510. He expects the sturgeon population to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the estimated sturgeon population, y, in x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =


explain how in 4 steps

Answer 1

y = 600(0.85)^x

Explanation (4 steps)
1. Identify the initial population (a): at x = 0, y = 600, so a = 600.
2. Find the yearly factor (b): b = population after 1 year ÷ initial = 510/600 = 17/20.
3. Write the exponential model: y = 600(17/20)^x, which as a decimal is y = 600(0.85)^x.
4. Check and interpret: for x = 1, y = 600·0.85 = 510; b = 0.85 means a 15% decrease each year.