Question

A species of dolphins is decreasing at a rate of 3.1% per year.if there are currently 20000 dolphins , many will there be in 30 years

Answer 1

Answer:

7892 dolphins

Step-by-step explanation:

let P denote the dolphin population.

-Notice this is an exponential decay and is denoted as:

$P_t=P_oe^{-rt}$

Where;

• $P_t$ is the population at time t
• t is the time
• r is the rate of decay or decrease in population
• $P_o$ is the initial population size.

#Given t=30yrs, $P_o$=20000 and r=3.1%, the population after 30 years is estimated as:

$P_t=P_oe^{-rt}\\\\=20000e^{-0.031\times 30}\\\\=7891.07\approx7892\ dolphins$

Hence, the dolphin population after 30yrs is approximately 7892