Answer:
a) $1000
b) 10 years
Step-by-step explanation:
Given exponential growth function:
[tex]A(t) = 1000 \times 2^{\frac{t}{10}}[/tex]
The given function A(t) represents the amount of money in the account at time t.
[tex]\hrulefill[/tex]
Part a
The initial amount invested is the value of A(t) when t = 0, which is the coefficient of the base term. Therefore, the initial investment was $1000.
[tex]\hrulefill[/tex]
Part b
To find the time it takes to double the money, we set A(t) equal to twice the initial investment ($2000) and solve for t:
[tex]1000\times 2^{\frac{t}{10}}=2000[/tex]
Divide both sides of the equation by 1000:
[tex]2^{\frac{t}{10}}=2[/tex]
Rewrite 2 as 2¹:
[tex]2^{\frac{t}{10}}=2^1[/tex]
Since the bases are the same, we can set the exponents equal to each other:
[tex]\dfrac{t}{10}=1[/tex]
Multiply both sides by 10:
[tex]t=10[/tex]
Therefore, it took 10 years to double the money.
