A city owned 300,000 cars at the end of 2000. It is estimated that 6% of the cars owned at the end of last year will be scrapped every year, and so will the number of new cars every year. In order to protect the urban environment, it is required that the number of cars in this city should not exceed 600,000, so the number of new cars should not exceed much.

Let k car be the upper limit, and the relationship should be satisfied. According to the meaning of the question, the recursive formula is obtained;

a 1=30

a(n+ 1)=an*( 1-6%) + k

Judging from the meaning of the problem, it is necessary to make any n have one

The following derivation leads to this formula.

a 1=30

A (n+1) = an * (1-6%)+k-formula1.

Structural geometric series, setting

a(n+ 1)+ t = 0.96*(an + t)

Reference equation 1

t=- 250k

That is, [a (n+1)-250k]/[an-250k] = 0.96.

For geometric series.

therefore

An = (a1-250k) * (0.96) (n-1)

=(30 -250k)*(0.96)^(n- 1)+250k

One; one

Obviously, the bigger n is, the smaller an is.

When n=2

Therefore (30-250k) * 0.96+250k < = 60.

solve

k & lt=3. 12

Taking k=3 is what you want.