Question

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

1. substitute ( t = 10: p = 4000 e^{0.03(10)} ).
2. simplify: ( p = 4000 e^{0.3} ).
3. evaluate: ( p = 4000(3.3) ).
4. final: ( p = 13,200 ).

line 4
no mistakes were made.
line 3
line 2
line 1

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