A colony of feral cats is increasing at a rate of 3 + 5t cats per year (where t is measured in years). By how much does the colony increase increase in size between the fourth and tenth years? 1. increases by 243 cats 2. increases by 238 cats 3. increases by 228 cats 4. increases by 233 cats 5. increases by 248 cats

3. increases by 228 cats

Step-by-step explanation:

The rate of the increase in cats is given by:

as this is the rate, we can write it as:

here t is the time in years. and S in the size of the colony

we're asked about the increase in size between the 10th and 4th year. So we need to know the sizes of the colony in those years.

We can find this out by integration. The above equation can be seen as a differential equation. Hence,

S(t) is the function of the size of the colony at time t. We need to find the differences of sizes between t = 10 and t = 4. Basically,

The C's will cancel out