Math homework help?

Need help ASAP with these problems (would be really helpful if anyone did the other ones in the picture too):

- Fish are known to travel in small groups known ascohorts. On average, the cohorts of a certain species of fish have been observed to have populations that decay asP(t)=P0e−^0.2t, where it is measured in years. What amount of time do we expect to pass in order for a cohort to shrink to 10%of its original size?

- In 1867, the U.S. purchased Alaska from Russia and paid a price of $7.2 million. Alaskahas 586,000 square miles of land. Assuming that the value of land increased continuously at around 3% per year, determine the price of one acre of land in the year 2019 (noting that 1 square mile is equivalent to 640 acres)? Estimate the land value of Alaska in 2019.

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  • Ian H
    Lv 7
    1 month ago
    Favorite Answer

    P(t)/Po= e^−(0.2t) = 0.1, take reciprocals of both sides 

    e^(t/5) = 10 

    t = 5ln(10) ~ 11.51 years 

     

    The value of land increased continuously at 3% per year 

    Let V be the value of the 586,000 square miles after n years 

    In millions of dollars, V = 7.2*(1.03)^n 

    2019 is 152 years after 1867 

    V = 7.2*(1.03)^152 = 643.562 million  

    Dividing by 640 to find v which is the value of 1 acre in 2019 

    v is just over $1 million, (actually about $1,005,566)  

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  • 1 month ago

    You can't take the formula and plug in the numbers ASAP yourself?

    0.1P0 = P0 e^(-0.2t)

    t = 5ln(10)

    f(t) = 7.2 (1.03)^t

    Where t is years after 1867 and f(t) is millions $.

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