Question

Twenty animals of a non-native species are introduced to an island. The number of these animals after t years is 500 P(t) = - How many years will it take until there are 250 of these animals on the island?

Answer 1

To find out how many years it will take until there are 250 animals on the island, we set up the equation P(t) = 20 * (0.5)^t and solve for t.

Step-by-step explanation:

To find out how many years it will take until there are 250 animals on the island, we need to set up an equation using the given information. The equation is P(t) = 20 * (0.5)^t, where P(t) represents the number of animals after t years. We want to find the value of t when P(t) = 250. We can set up the equation as follows:

250 = 20 * (0.5)^t

To solve for t, divide both sides of the equation by 20:

12.5 = (0.5)^t

Next, take the logarithm of both sides of the equation:

log(12.5) = log((0.5)^t)

Using the logarithmic property log(a^b) = b * log(a), we can rewrite the equation as:

log(12.5) = t * log(0.5)

Now, divide both sides of the equation by log(0.5):

t = log(12.5) / log(0.5)

Using a calculator, we can find that t is approximately 4.64 years. Therefore, it will take about 4.64 years until there are 250 animals on the island.