Initial Amount: 10 Rate of Growth: 40 % Value When t=5: ≈ 53.8
Practice makes perfect
Let's start by recalling the general formulas for exponential growth and exponential decay functions.
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Exponential Growth & Exponential Decay [0.8em]
y=a(1+r)^t & y=a(1-r)^t
In both cases, a>0 is the initial amount and r>0 is the rate of growth or decay written in decimal form. Moreover, for exponential decay, r is less than 1. Let's consider the given function.
y= 10(1+ 0.4)^t
Our function represents exponential growth, with an initial amount a= 10 and a rate of growth r= 0.4. To rewrite the rate of growth as a percent, we move the decimal point two places to the right.
r=0.4 ⇔ r=40 %
Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula.
