Question 1078701
the formula is actually:


A = P * (1 + .07) ^ T


since 1 + .07 is equal to 1.07, the formula becomes:


A = P * 1.07 ^ T


replace P with 16,000 and replace A with 22,400 and the equation becoms:


22,400 = 16,000 * 1.07 ^ T


divide both sides of the equation by 16,000 to get:


22,400 / 16,000 = 1.07 ^ T


simplify to get:


1.4 = 1.07 ^ T


take the log of both sides of the equation to get:


log(1.4) = log(1.07 ^ T)


this is equivalent to:


log(1.4) = T * log(1.07)


divide both sides of the equation by log(1.07) to get:


log(1.4) / log(1.07) = T


solve for T to get T = 4.973085396


16,000 should grow to 22,400 in 4.973085396 years.


to confirm, replace T in the original equation to get:


22,400 = 16,000 * 1.07 ^ (4.973085396)


use your calculator to evalutat 16,000 * 1.07 ^ (4.973085396)


you will find that it is equal to 22,400, confirming the solution is correct.


the peoerty of logs that allows you to solve this equation is:


log(b^x) = x * log(b)


for example:


log(2^5) = 5 * log(2)


use your calculator to get log(2^5) and use your calculator to get 5 * log(2)


both answers should be the same, namely 1.505149978