Question

two dams, when opened, release water at different rates. the following functions represent the amounts of water the dams release over $t$ minutes:dam a$f(t) = 5^t - 7t - 1$dam b$g(t) = 3t^2 + 4t + 9$which function represents the difference in the amounts of water released, $h(t) = f(t) - g(t)$?$h(t) = 3t^2 - 5^t + 11t + 10$$h(t) = 2t^2 - 11t - 10$$h(t) = 5^t - 3t^2 - 3t + 8$$h(t) = 5^t - 3t^2 - 11t - 10$

Explanation:

Step1: Substitute functions into $h(t)$

$h(t) = (5^t - 7t - 1) - (3t^2 + 4t + 9)$

Step2: Distribute the negative sign

$h(t) = 5^t - 7t - 1 - 3t^2 - 4t - 9$

Step3: Combine like terms

$h(t) = 5^t - 3t^2 + (-7t - 4t) + (-1 - 9)$
$h(t) = 5^t - 3t^2 - 11t - 10$

Answer:

$h(t) = 5^t - 3t^2 - 11t - 10$ (the fourth option)