Exponential model for bonobo population decline (start 40,000; 1-year drop to 39,200)

Create an exponential model y = a(b)^x for a bonobo population that starts at 40,000 and decreases to 39,200 after 1 year, then estimate the population after 7 years (rounded to the nearest hundred).

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Step 1 — Write the model form
We use y = a(b)^x, where a is the initial population and b is the annual decay factor.

Step 2 — Find a and b
Initial population: a = 40,000.
After 1 year: 39,200 = 40,000·b, so b = 39,200 / 40,000 = 0.98.

Exponential model:
y = 40000(0.98)^x

Step 3 — Estimate after 7 years
y(7) = 40000(0.98)^7 ≈ 40000·0.868125533 ≈ 34,725.02

Rounded to the nearest hundred: 34,700 bonobos.

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