High School

Mites are discovered in a peach orchard. The Department of Agriculture has determined that the population of mites, \( N(t) \), \( t \) hours after the orchard has been sprayed, is approximated by:

\[ N(t) = 1600 - 3t \ln(0.07t) - t \]

What is the maximum number of mites in the peach orchard? Round to the nearest whole number.

Answer :

The maximum number of mites in the peach orchard are 1564

Given that,

There are found to be mites in a peach orchard. According to research conducted by the Department of Agriculture, the number of mites t hours after the orchard has been sprayed is roughly represented by the equation N(t)=1600-3tln(0.07t)-t

To find : What is the maximum number of mites in the peach orchard? Round to the nearest whole number.

N(t)=1600-3tln(0.07t)-t

N(19)=1600-3(19)ln(0.07(19))-(19)

N(19)=1600- 16.255 - 19

N(19)=1564.74

N(19)≈1564

Therefore, the maximum number of mites in the peach orchard are 1564

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