A late is stocked with fish. The fish population is modeled by the equation P=10√(t) + 2t +336 where t is the number of days since the fish were first introduced into the lake. Determine the number of days it will take for the population to reach 300 fish. Give your answer in exact form and then as a decimal rounded to two decimal places.

Question

A late is stocked with fish.  The fish population is modeled by the equation P=10√(t) + 2t +336 where t is the number of days since the fish were first introduced into the lake.  Determine the number of days it will take for the population to reach 300 fish.  Give your answer in exact form and then as a decimal rounded to two decimal places.

campbell_st · Answer

ok... so you need to set P = 300 and solve for t

$$300 = 10\sqrt{t} + 2t + 336$$

campbell_st · Answer

then you can have 

$$-2t - 36 = 10\sqrt{t}$$

divide both sides by t

$$\frac{-2t - 36}{10} = \sqrt{t}$$

hope this helps

anonymous · Answer

$$P = 10\sqrt{t} + 2t + 336$$where 'P' is population and 't' is no. of days.
Given population = 300, then:
$$300 = 10\sqrt{t}+2t+336$$$$10\sqrt{t} = -2t - 36$$Squaring both sides:$$100t = 4t^{2}-144t +1296$$$$4t^{2}-244t+1296 = 0$$$$4(t^{2} -61t + 324) = 0$$$$t^{2}-61t+324 =0$$ @AdriRules Now factorize.

anonymous · Answer

Thank you @curiousshubham and @campbell_st !

anonymous · Answer

@AdriRules you are welcomed..