find the first mistake in solving for a population in the tenth year, using ( p(t)=4000 e^{0.03 t} ).\n1…

find the first mistake in solving for a population in the tenth year, using ( p(t)=4000 e^{0.03 t} ).\n1. substitute ( t = 10: p = 4000 e^{0.03(10)} ).\n2. simplify: ( p = 4000 e^{0.3} ).\n3. evaluate: ( p = 4000(3.3) ).\n4. final: ( p = 13,200 ).\nline 4\nno mistakes were made.\nline 3\nline 2\nline 1

find the first mistake in solving for a population in the tenth year, using ( p(t)=4000 e^{0.03 t} ).\n1. substitute ( t = 10: p = 4000 e^{0.03(10)} ).\n2. simplify: ( p = 4000 e^{0.3} ).\n3. evaluate: ( p = 4000(3.3) ).\n4. final: ( p = 13,200 ).\nline 4\nno mistakes were made.\nline 3\nline 2\nline 1

Answer

Explanation:

Step1: Analyze Line 1

Substitute (t = 10) into (P(t)=4000e^{0.03t}), we get (P = 4000e^{0.03\times10}). This step is correct.

Step2: Analyze Line 2

Simplify (0.03\times10 = 0.3), so (P = 4000e^{0.3}). This step is correct.

Step3: Analyze Line 3

The value of (e^{0.3}\approx1.34986), not (3.3). So the mistake is in Line 3.

Answer:

Line 3