# Math

7) A population of ants is growing at a rate of 8% a year. If there are 160 ants in the initial population, find
the number of ants after 6 years.

1. 👍
2. 👎
3. 👁
1. 8% + 100% = 108% = 108 / 100 = 1.08

The n-th term of a geometric sequence with initial value a1 and common ratio r is given by:

an = a1 ∙ r ⁿ⁻¹

In tis case :

a1 = 160

r = 1.08

Need to notice that term two is after one year, so term 7 will be after 6 years.

n = 7

so:

a6 = a1 ∙ r⁷⁻¹

a6 = 160 ∙ r⁶

a6 = 160 ∙ 1.08⁶

a6 = 160 ∙ 1.586874322944

a6 = 253.89989167104

The number of ants after 6 years will be 253.

1. 👍
2. 👎
2. Why plusing this 100 % and rate of 8%

1. 👍
2. 👎

## Similar Questions

1. ### math(A.P/G.P)

the population of a country was 55 crores in 2005 and is growing at 2% p.a C.I , the population in the year 5015 is estimated as ? a)5705 b)6005 c)6700

2. ### Pre-Calc

The fox population in a certain region has a continuous growth rate of 9 percent per year. It is estimated that the population in the year 2000 was 23400. (a) Find a function that models the population t years after 2000 (t=0 for

3. ### calculus

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after

4. ### Algebra

A population of ants is growing at a rate of 10% per month. What is the growth factor?

1. ### Math

Which scenario can be modeled by a linear function? A - The area of a circle A can be determined using length of the diameter of the circle D B - the number of gallons of water used W is based on the number of minutes T a fire

the population of a town is decreasing at a rate of 1.8% per year. The current population of the own in 12000. a)write and equation that models the population of the town b)how long will it take for the population to decline to

3. ### math

the population of a town is declining at a rate of 4.1% per year. the current population is 25000. 1)what will the population be in 7 years. 2) how long will it take the population to reach 15000?

4. ### math

the population of Smallville in the year 1890 was 6250.assume the population increased at a rate of 2.75% per year. predict when the population reached 50,000 I'm not suppose to use logs to find the answer :(

1. ### Algebra 2

The fly population on an island is declining at a rate of 1.7% per year. The population was 4600 in the year 2016. Which answer is the best prediction of the population in the year 2023? 4010

2. ### Math

The population of Andhra Pradesh was 5.4 * 10^7 in 1988. If the population was growing at a constant rate of 2.4% per annum, what was the population in 2008 A.D ( Given that (1.024)^20 = 1.60694)

3. ### Calculus

Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.21 percent a year and that the 1988 population was 6.8 million, write an expression for the population as a function of time in years. (Let

4. ### Calculus

A population is currently 400 and growing at a rate of 6% per year. (a) Write a formula for the population P as a function of time t in years: P(t)= 400(1+.06)^t (b) If the population continues this trend, what will it be in ten