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The size of a population, P, can be calculated with this equation.
P = Po(1 + r)
In the equation, Po represents the initial population size, rrepresents the population's growth rate, and t represents the time in years.
A population of frogs in a pond currently has 50 individuals and grows at a rate of 30 percent per year. It will take this
population approximately
years to double in size.

Sagot :

ttaimi1458

Answer:

2.64

Step-by-step explanation:

When the population doubles in size, it will have 100 individuals. So replace P with 100, ^p0(0 is a bottom exponent like you would write a log) with 50, and r with 0.3 in the population growth equation to solve for the number of years, t.

100=50(1+0.3)^t

100=50(1.3)^t

Isolate the exponential term. Then rewrite the equation as a logarithmic equation, and solve for t using the properties of logs.

2=1.3^t

log 1.3 2=t(1.3 low exponent again like explained)

log2/log(1.3)=t

t≈2.64

So it will take this population approximately 2.64 years to double in size.

Using the formula of compounding annually, given that population of frogs in a pond currently has 50 individuals and grows at a rate of 30 percent per year. It will take this population approximately 2.64 years to double in size.

What is compounding annually?

Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid.

[tex]P= Po(1 + \frac{R}{100})^{n}[/tex]

Where,

P = size of population

Po = Initial population

R = Rate of growth

t = time period

[tex]100 = 50(1 + \frac{30}{100})^{t}\\ \\2 = (1.3)^{t}\\\\t = log_{1.3} 2\\\\t = 2.64[/tex]

It will take 2.64 years for the population to double in size.

Learn more about compounding annually here

https://brainly.com/question/24095823

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