In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal?
A)1982
B)1978
C)1983
D)1984
E)1981

Question

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by  and  , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal? ​
A)1982 
B)1978 
C)1983 
D)1984 
E)1981

Quizplus · Accepted Answer

We need to find the year when B(x) = H(x). 
11eb0d3b_979a_8672_9790_8fc3059eebeb_TB1243_11 = 17.7(1.042)^x 
11eb0d3b_979a_8673_9790_85c78084a00c_TB1243_11 = 6.7(1.063)^x

Setting them equal to each other, we get: 
17.7(1.042)^x = 6.7(1.063)^x

Dividing both sides by 6.7(1.063)^x, we get: 
2.641 = (1.042/1.063)^x

Taking the logarithm of both sides, we get: 
log(2.641) = x*log(1.042/1.063)

Solving for x, we get: 
x = log(2.641)/log(1.042/1.063) ≈ 12.97

Adding x years to December 31st, 1970, we get: 
1970 + 12.97 ≈ 1983

Therefore, the numbers of black and Hispanic children were equal in 1983.

In the United States Between 1970 and 2002, the Number