Question

A quantity with an initial value of 4000 grows exponentially at a rate of 0.05% every 5 decades. What is the value of the quantity after 1 year, to the nearest hundredth?

Answer 1

The value of the quantity after 1 year, to the nearest hundredth is 4000.00

The exponential form of an equation

The standard exponential equation is eexpressed as:

$P(t)=P_0e^{kt}$

Given the following parameters

$P_0=4000\\r =0.0005\\t = \frac{1}{50} =0.02 (yearly)$

Substitute into the formula to have:

$P(t)=4000e^{0.0005(0.02)}\\P(1)=4000e^{0.00001}\\P(1)=4000$

Hence the value of the quantity after 1 year, to the nearest hundredth is 4000.00

Learn more on exponential equations here: brainly.com/question/12940982