BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.5, Problem 116E
To determine

The number of days it will take for the fish population to reach 500.

Expert Solution

Answer to Problem 116E

The number of days it will take for the fish population to reach 500 is 89days_.

Explanation of Solution

Given:

The fish population in the tank is modeled by the formula P=3t+10t+140, where, P is number of fish and t is the number of days since the fish were first introduced into the pond.

Formula used:

Quadratic formula:

The solution of a quadratic equation of the form ax2+bx+c=0,a0 can be obtained by using the quadratic formula x=b±b24ac2a.

Calculation:

Substitute 500 for P in P=3t+10t+140 to obtain the number of days it will take for the fish population to reach 500.

500=3t+10t+1403t+10t+140500=03t+10t360=03(t)2+10t360=0

Let x=t. Substitute x for t in 3(t)2+10t360=0.

3(x)2+10x360=03x2+10x360=0

Use Quadratic formula to find the value of x.

Substitute 3 for a, 10 for b and 360 for c in x=b±b24ac2a.

x=(10)±(10)24×3×(360)2×3=10±100+43206=10±44206

Simplify the above equation as follows.

x=10±66.486=10+66.486or 1066.486=56.486or 76.486=9.41or 12.75

Note that, the number of days must be positive.

Therefore, substitute t for x in x=9.41.

t=9.41t=(9.41)2t=88.5481t89

Thus, the number of days it will take for the fish population to reach 500 is 89days_.

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