# math

The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 310 rabbits.

(a) Express the population of the colony of rabbits, P , as a function of time, t , in years.

(b) Use the graph to estimate how long it takes for the population of rabbits to reach 1000 rabbits.

1. 👍 1
2. 👎 0
3. 👁 1,686
1. P = A e^kt
A = 5 is given when t = 0 (because e^0 = 1)
P = 5 e^kt
310 = 5 e^5k
62 = e^5k
ln 62 = 5 k
5 k = 4.127
k = .8254
so
P = 5 e^.8254 t

now if P = 1,000
200 = e^.8254 t
ln 200 = 5.298 = .8254 t
t = 6.42 years

1. 👍 2
2. 👎 2

## Similar Questions

1. ### World History

Which helped the Jamestown colony continue? *The acquisition of gold held by the Powhatan tribe provided the viability of the colony *The production of tobacco as a cash crop led to the successful support of the colony *The

2. ### Science

Multiplying Rabbits Suppose that a pair of rabbits produces six offsrping: 3 males and 3 females. Assumes that no offspring die. 1. If each pair of rabbits breeds only once, how many offspring would be produced each year for 5

3. ### Calculus

The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 , for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain

4. ### Algebra-Problems

Please help with my word problems? Solve the problem. The rabbit population in a forest area grows at the rate of 6% monthly. If there are 260 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be

1. ### pre calc

The population of a colony of mosquitoes grows exponentially according to the function P(t) = P0ekt 1. If there are 1,000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days? 2. How

2. ### Algebra 2

A certain population of rabbits is doubling its population every 2 months. The original population started with only 20 rabbits. A biologist studying the population found that the equation 1000=20(2)^t shows how many months, t, it

3. ### Calculus

The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 ,for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical

4. ### AP Environmental Science

Why is it necessary to eliminate absolutely all invasive fire ant colonies to eradicate the invasive population? A)Every colony has a major impact on native flora and fauna. B)Because the last colony found is the one housing the

1. ### math check

21% of a certain breed of rabbits are born with long hair. What is the probability that in a litter of 12 rabbits, exactly 2 will have long hair? (Give your answer correct to three decimal places.) 1=.21=.79 0.79^12=0.05909

2. ### Math

1. A colony of bacteria grows exponentially according to the function where N is measured in grams and t is measured in days. N(t)=100e^0.045t You may use graphical method or algebraic method. Please show work if algebraic or show

3. ### Precalc

A colony of 1000 weevils grows exponentially to 1750 in one week. a) At what continuous rate is the population growing? b) How many weeks does it take for the weevil population to reach 3000?

4. ### algebra

lenny anf george started with 2 rabbits and each month the number of rabbits doubled since each pair of rabbits produced another pair of rabbits. what is an eqaution for this situation ? Lenny and george now have 30 million