Question

On the planet Maximillian live Sprogs and Graks. Initially there were 4000 sprogs and 500 Graks. The population of Sprogs doubles every 10 years and that of Graks doubles every 5 years. a. How many Graks were there after 2

2
1
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years? Graks b. When are there as many Sprogs as Graks? years later

Answer 1

a. The population of Graks doubles every 5 years, so after 22 years, the population would have doubled 4 times (22/5 = 4.4, but we only count full periods of 5 years). So the number of Graks after 22 years would be 500 * 2^4 = 8000.

b. Let's find out when the number of Sprogs and Graks will be equal. Let n be the number of years it takes for the populations to be equal. Then we can write the equation:

4000 * 2^(n/10) = 500 * 2^(n/5)

Dividing both sides by 500, we get:

8 * 2^(n/10) = 2^(n/5)

Taking the logarithm base 2 of both sides, we get:

log2(8) + n/10 = n/5

Solving for n, we get:

n = (10 * log2(8)) / (1/5 - 1/10) = (30 * log2(2)) / (1/10) = 300

So there will be as many Sprogs as Graks after **300 years**.