a population of trout is dying at an exponential rat of 13% each day. If there were 400 trout in the pond on Monday, how many are still alive on Friday?

Question

Please show all work

Answer 1

The formula for calculating the result of decay, or exponential decrease, is

 

P = P₀(1 - r)ⁿ

 

P is the number after the period being looked at

P₀ is the initial number, or the initial population -- 400

r is the rate of decline per period, as a decimal, not a percentage -- 13% or 0.13

n is the number of periods -- 4, since Friday is 4 days after Monday

 

So P = 400 (1 - 0.13)⁴ = 400 * .87⁴ = 229.16.  Since there can't be a fraction of a trout, you'd round this to the nearest whole number, or 229.