Anest of ants initially contains 500 individuals. the population is increasing by 12% each week.

a) how many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)how many weeks will it take for the ant population to reach 2000.

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

a) (i) If x = 10 weeks,

The number of ants would be,

(ii) If x = 20 weeks,

The number of ants would be,

b) If A = 2000

Taking log both sides,

log(4) = xlog(1.12)

⇒ x =  12.23 ≈ 12 weeks

135 is your answer

step-by-step explanation:

try 180 times three then divide that number by 4 (sides) to get your answer. im glad to : )

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.