Initial Amount: 25 Rate of Growth: 20 % Value When t=5: ≈ 62.2
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 rewrite the given function to match one of the above formulas.
Our function represents exponential growth, with an initial amount a= 25 and a rate of growth r= 0.2. To rewrite the rate of growth as a percent, we move the decimal point two places to the right.
r=0.2 ⇔ r=20 %
Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula.
<deduct>
y=25(1.2)^t
t= 5
y=25(1.2)^{{\color{#0000FF}{5}}}
expand Evaluate right-hand side
Calculate power
y=25(2.48832)
Multiply
dnapxe
y=62.208
Round to 1 decimal place(s)
y\approx 62.2
</deduct>
