brad studies bottlenose dolphins and wants to estimate the population in a certain region. brad catches 67…

brad studies bottlenose dolphins and wants to estimate the population in a certain region. brad catches 67 dolphins, marks them, and releases them. later on, brad catches 380 dolphins and observes that 38 of them are marked. to the nearest whole number, what is the best estimate for the dolphin population?

brad studies bottlenose dolphins and wants to estimate the population in a certain region. brad catches 67 dolphins, marks them, and releases them. later on, brad catches 380 dolphins and observes that 38 of them are marked. to the nearest whole number, what is the best estimate for the dolphin population?

Answer

Explanation:

Step1: Set up proportion

Let $x$ be the total dolphin population. The proportion is $\frac{\text{marked dolphins}}{\text{total population}}=\frac{\text{recaptured marked dolphins}}{\text{recaptured dolphins}}$, so $\frac{67}{x}=\frac{38}{380}$.

Step2: Cross - multiply

Cross - multiplying gives $38x = 67\times380$.

Step3: Solve for $x$

First, calculate $67\times380 = 25460$. Then $x=\frac{25460}{38}=670$.

Answer:

670