4.1 Homework Score: $42 / 100 \quad 6 / 15$ answered Question 14 The rat population in a major metropolitan city is given by the formula $n(t)=78 e^{0.01 t}$ where $t$ is measured in years since 2002 and $n(t)$ is measured in millions. What was the rat population in 2002 (Enter answer in millions, ie: \#\#\#\#\#,\#\#)? rats What does the model predict the rat population was in the year 2018 (Enter answer in millions, ie: \#\#,\#\#,\#\#)? rats Submit Question

Step 1 ：The question is asking for the rat population in the year 2002 and 2018. The formula given is \(n(t)=78 e^{0.01 t}\) where \(t\) is measured in years since 2002 and \(n(t)\) is measured in millions.

Step 2 ：To find the rat population in 2002, we need to substitute \(t=0\) into the formula because the year 2002 is the starting point.

Step 3 ：Substituting \(t=0\) into the formula, we get \(n(0)=78 e^{0.01 \times 0} = 78\). So, the rat population in 2002 was 78 million.

Step 4 ：To find the rat population in 2018, we need to substitute \(t=2018-2002=16\) into the formula because the year 2018 is 16 years after 2002.

Step 5 ：Substituting \(t=16\) into the formula, we get \(n(16)=78 e^{0.01 \times 16} = 91.53\). So, the rat population in 2018 was approximately 91.53 million.

Step 6 ：Final Answer: The rat population in 2002 was \(\boxed{78}\) million and in 2018 was approximately \(\boxed{91.53}\) million.