Question

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

Answer 1

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

Explanation:

Given;

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

Converting the given function to log;

`I(t) = 27,992(1.017)^t \\\\(I(t))/(27,992) = (1.017)^t\\\\Log_(1.017) ( (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) ( (I(t))/(27,992) )= t\\\\Log_(1.017) ( (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