Question

I(t) = 27, 992 * (1.017) ^ t covert to log

Answer 1

Answer:

By 2034 Texas per capita income would reach at least $50,000

Step-by-step explanation:

Given;

$I(t) = 27,992(1.017)^t$

Converting the given function to log;

$I(t) = 27,992(1.017)^t \\\\\frac{I(t)}{27,992} = (1.017)^t\\\\Log_{1.017} ( \frac{I(t)}{27,992} )= t \\\\(Based \ on \ log \ rule; if \ a = b^y , in \ log \ it \ will \ be \ written \ as, Log_b \ a = y)$

(B) When I(t) = $50,000, the time "t" will become;

$Log_{1.017} ( \frac{I(t)}{27,992} )= t\\\\Log_{1.017} ( \frac{50,000}{27,992} ) = t\\\\Log_{1.017} (1.7862) = t\\\\34.4 \ years = t$

Thus, by 2034 Texas per capita income would reach at least $50,000