Question

A Population of spiders a lab, p(x), can be modeled by the function p(x) =400(1.012)^x, where X represents the number of days since population was first counted. When will the population be 550?

Answer 1

Population becomes 550 in 27 days

Step-by-step explanation:

The population of spiders in a lab is modeled by the function $P(x)=400(1.012)^{x}$, where $x$ represents the number of days since population was first counted.

   Consider that after $t$ days, the population of spiders has grown to 550. We need to find such $t$.

$550=400(1.012)^{t}$

$(1.012)^{x}=\frac{550}{400}=1.375$

Applying logarithm on both sides,

$xlog_{10}(1.012)=log_{10}(1.375)$

$x=\frac{log_{10}(1.375)}{log_{10}(1.012)}=26.6967$

∴ It takes about 27 days for the population to become 550.